{"id":27926,"date":"2023-04-26T03:21:16","date_gmt":"2023-04-26T03:21:16","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27926"},"modified":"2023-08-03T04:17:59","modified_gmt":"2023-08-03T04:17:59","slug":"interior-angles-definition-theorem-formula-types-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles","title":{"rendered":"Interior Angles &#8211; Definition, Theorem, Formula, Types, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-cf562680-b8df-4972-9bc0-e40551537438\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles#0-what-are-interior-angles>What Are Interior Angles?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles#3-what-are-the-types-of-interior-angles>What Are the Types of Interior Angles?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles#9-sum-of-interior-angles-formula>Sum of Interior Angles Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles#14-solved-examples-on-interior-angles>Solved Examples on Interior Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles#15-practice-problems-on-interior-angles>Practice Problems on Interior Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles#16-frequently-asked-questions-on-interior-angles>Frequently Asked Questions on Interior Angles<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-interior-angles\">What Are Interior Angles?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The term \u201cinterior angles\u201d in geometry can be used in two different contexts.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Interior angle formed when two parallel lines are cut by a transversal<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Interior angles formed inside a polygon (a shape)<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s explore the meaning of interior angles with respect to each of these cases along with types, different formulas and examples.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-interior-angles-definition\">Interior Angles Definition<\/h3>\n\n\n<div class=\"ub-styled-box ub-notification-box custom_note_box\" id=\"ub-styled-box-173c2369-c355-41da-8e7c-c290baf1bd6b\">\n\n\n<p class=\"eplus-wrapper\">The angles that lie inside a polygon are called interior angles of a polygon. When two parallel lines are cut by a transversal, the angles that lie between the two parallel lines are known as interior angles.<\/p>\n\n\n<\/div>\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"2-interior-angles-formed-when-two-parallel-lines-are-cut-by-a-transversal\">Interior Angles Formed When Two Parallel Lines Are Cut By a Transversal<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">The angles that lie in the area enclosed between two parallel lines cut by a transversal are also called interior angles.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Observe the image shown below.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, the lines L1 and L2 are parallel lines.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">L is the transversal that intersects these lines.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\angle 1,\\; \\angle 4,\\; \\angle 2,\\; \\angle 3$ are interior angles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"381\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/interior-angles-formed-by-a-transversal-cutting-two-parallel-lines.png\" alt=\"Interior angles formed by a transversal cutting two parallel lines\" class=\"wp-image-32604\" title=\"Interior angles formed by a transversal cutting two parallel lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/interior-angles-formed-by-a-transversal-cutting-two-parallel-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/interior-angles-formed-by-a-transversal-cutting-two-parallel-lines-300x184.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We will refer to this image to understand the types of the interior angles.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-the-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_add_angles_pt.png\" alt=\"Add the Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add the Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-in-multiples-of-10-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_1_pt.png\" alt=\"Draw Angles in Multiples of 10 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles in Multiples of 10 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-nearest-5-and-1-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_2_pt.png\" alt=\"Draw Angles Nearest 5 and 1 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles Nearest 5 and 1 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-using-a-protractor\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_protractor_pt.png\" alt=\"Draw Angles Using a Protractor Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles Using a Protractor Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-right-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_right_angle_1_pt.png\" alt=\"Find Right Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Right Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-perimeter-of-the-squared-and-the-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_rectangle_2_pt.png\" alt=\"Find the Perimeter of the Squared and the Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Perimeter of the Squared and the Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-angles-by-their-types\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_types_of_angle_pt.png\" alt=\"Identify Angles by their Types Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Angles by their Types Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            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});\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-what-are-the-types-of-interior-angles\">What Are the Types of Interior Angles?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Two types of interior angles are formed when a transversal cuts two parallel lines:&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Co-interior angles or Same Side Interior Angles<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Alternate interior angles&nbsp;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-same-side-interior-angles-co-interior-angles\">Same Side Interior Angles (Co-interior Angles)<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">These are pairs of non-adjacent angles that lie on the same side of the transversal. The sum of two co-interior angles is $180^\\circ$. They are supplementary.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The angle pairs that form same-side interior angles in the above image are&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\\angle 1$ and $\\angle 4$ such that $\\angle 1 + \\angle 4 = 180^\\circ$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\angle 2$ and $\\angle 3$ such that $\\angle 2 + \\angle 3 = 180^\\circ$<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-alternate-interior-angles\">Alternate Interior Angles<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Alternate interior angles lie on the opposite sides of the transversal. <strong>The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The angle pairs that form alternate interior angles in the above image are:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\\angle 1$ and $\\angle 3$ such that $\\angle 1 =\\angle 3$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">$\\angle 2$ and $\\angle 4$ such that $\\angle 2 =\\angle 4$<\/li>\n<\/ul>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/count-sides-and-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/count-sides-and-angles.jpeg\" alt=\"Count Sides and Angles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rectangles-and-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/separate-out-the-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/separate-out-the-triangles.jpeg\" alt=\"Separate Out the Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-interior-angles-of-a-polygon\">Interior Angles of a Polygon<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The angles that lie inside a polygon formed by the sides are called interior angles.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The following image shows interior angles of a triangle and a pentagon.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Note that the number of interior angles in a polygon is always equal to the number of sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Interior angles examples:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"281\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/Interior-angles-of-a-polygon.png\" alt=\"Interior angles of a polygon\" class=\"wp-image-32606\" title=\"Interior angles of a polygon\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/Interior-angles-of-a-polygon.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/Interior-angles-of-a-polygon-300x136.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-interior-angles-of-a-triangle\">Interior Angles of a Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A triangle has three interior angles. The sum of three interior angles of a triangle always sums up to 180\u00b0. If we bisect these angles, the angle bisectors meet at a point called the incenter.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the sum of interior angles of a triangle is 180\u00b0, only one right angle or only one obtuse angle is possible in each triangle.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-classification-of-triangles-based-on-interior-angles\">Classification of Triangles Based on Interior Angles<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Acute Triangle:<\/strong> A triangle which has all three interior angles as acute is called an acute triangle.<br><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>Obtuse Triangle: <\/strong>A triangle whose one interior angle is an obtuse angle and other two angles are acute is known as an obtuse triangle.<br><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>Right Triangle:<\/strong> A triangle which has one interior angle is a right angle and other two angles are acute is known as a right-angled triangle.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">A triangle in which all the angles are of equal measure is called an equiangular triangle. It basically is the equilateral triangle in which all interior angles are 60 degrees.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"270\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/classification-of-triangles-based-on-interior-angles.png\" alt=\"Classification of triangles based on interior angles\" class=\"wp-image-32607\" title=\"Classification of triangles based on interior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/classification-of-triangles-based-on-interior-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/classification-of-triangles-based-on-interior-angles-300x131.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-sum-of-interior-angles-formula\">Sum of Interior Angles Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">If we take the simplest polygon, a triangle, or any polygon with n sides, all the sides of a polygon will create interior and exterior angles.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As per the angle sum theorem, the sum of all the three interior angles of a triangle is equal to $180^\\circ$. Let us now see the formula to calculate the sum of interior angles of any polygon with \u201cn\u201d sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Sum of interior angles formula:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Sum of interior angles of a polygon $= S = (n \\;\u2212\\; 2) \\times 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $S =$ Sum of interior angles&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$n =$ number of sides of the polygon.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us apply this formula on a triangle and check the result:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$S = (n\\;\u2212\\;2) \\times 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$S = (3\\;\u2212\\;2) \\times 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$S = 1 \\times 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$S = 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us look at a table to understand how to use the same formula to calculate the sum of the interior angles of polygons:<\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-html-table\"><tbody><tr class=\"wj-html-tr\"><td><strong>Polygon<\/strong><\/td><td><strong>Number of Sides (n)<\/strong><\/td><td><strong>Sum of Interior Angles<\/strong><\/td><\/tr><tr><td>Triangle<\/td><td>3<\/td><td>$180^\\circ\\times(3\\;-\\;2) = 180^\\circ$<\/td><\/tr><tr><td>Quadrilateral<\/td><td>4<\/td><td>$180^\\circ\\times(4\\;-\\;2) = 360^\\circ$<\/td><\/tr><tr><td>Pentagon<\/td><td>5<\/td><td>$180^\\circ\\times(5\\;-\\;2) = 540^\\circ$<\/td><\/tr><tr><td>Hexagon<\/td><td>6<\/td><td>$180^\\circ\\times(6\\;-\\;2) = 720^\\circ$<\/td><\/tr><tr><td>Heptagon<\/td><td>7<\/td><td>$180^\\circ\\times(7\\;-\\;2) = 900^\\circ$<\/td><\/tr><tr><td>Octagon<\/td><td>8<\/td><td>$180^\\circ\\times(8\\;-\\;2) = 1080^\\circ$<\/td><\/tr><tr><td>Nonagon<\/td><td>9<\/td><td>$180^\\circ\\times\u2a2f(9\\;-\\;2) = 1260^\\circ$<\/td><\/tr><tr><td>Decagon<\/td><td>10<\/td><td>$180^\\circ\\times(10\\;-\\;2)= 1440^\\circ$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-finding-an-unknown-interior-angle\">Finding an Unknown Interior Angle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We use the \u201cSum of Interior Angles Formula\u201d to find an unknown interior angle of a polygon.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us consider an example to find the missing angle $\\angle x$ in the following quadrilateral.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"427\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/a-96-degree-angle-and-one-missing-interior-angle.png\" alt=\"A 96 degree angle, and one missing interior angle\" class=\"wp-image-32608\" title=\"A 96 degree angle, and one missing interior angle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/a-96-degree-angle-and-one-missing-interior-angle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/a-96-degree-angle-and-one-missing-interior-angle-300x207.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">From the above given interior angles of a polygon table, the sum of the interior angles of a quadrilateral is $360^\\circ$. Two of the interior angles of the above quadrilateral are right angles.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, we get the equation:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$90 + 90 + 96 + x = 360^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us solve this to find x.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$276 + x = 360$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = 360\\;-\\;276 = 84^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the missing interior angle x is $84^\\circ$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-interior-angles-of-regular-polygons\">Interior Angles of Regular Polygons<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">When all the sides and angles of a polygon are congruent, it is known as a regular polygon. Let us look at some examples of regular polygons:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"535\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/regular-polygons-examples.png\" alt=\"Regular polygons examples\" class=\"wp-image-32609\" title=\"Regular polygons examples\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/regular-polygons-examples.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/regular-polygons-examples-300x259.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We already studied that the formula to calculate the sum of the interior angles of any polygon of \u201cn\u201d sides is $180^\\circ(n\\;-\\;2)$. As we know that there are \u201cn\u201d angles in a regular polygon which have \u201cn\u201d sides.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since all the interior angles of a regular polygon are equal, each interior angle can be calculated by dividing the sum of the angles by the number of sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Each interior angle of a regular polygon <\/strong>$= \\frac{180^\\circ \\times (n\\;-\\;2)}{n}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us use this formula to calculate the interior angle of a regular hexagon. We know that the number of sides of a hexagon is 6 (Here, $n = 6$).&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Each interior angle of a regular hexagon $= \\frac{180^\\circ\\times(n\\;-\\;2)}{n}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{180^\\circ\\times(6\\;-\\;2)}{6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{180\\times4}{6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= \\frac{720^\\circ}{6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$=120^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, each interior angle of a regular hexagon is equal to $120^\\circ$.<\/p>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-html-table\"><tbody><tr class=\"wj-html-tr\"><td><strong>Regular Polygon<\/strong><\/td><td><strong>Sides(n)<\/strong><\/td><td><strong>Sum of Interior Angles (S)<\/strong><\/td><td><strong>Measure of Each Interior Angle<\/strong><\/td><\/tr><tr><td>n-sided polygon<\/td><td>n<\/td><td>$180^\\circ\\times(n\\;-\\;2)$<\/td><td>$\\frac{180^\\circ(n\\;-\\;2)}{n}$<\/td><\/tr><tr><td>Triangle<\/td><td>3<\/td><td>$180^\\circ(3\\;-\\;2) = 180^\\circ$<\/td><td>$\\frac{180^\\circ}{3} = 60^\\circ$<\/td><\/tr><tr><td>Square<\/td><td>4<\/td><td>$180^\\circ(4\\;-\\;2) = 360^\\circ$<\/td><td>$\\frac{360^\\circ}{4} = 90^\\circ$<\/td><\/tr><tr><td>Pentagon<\/td><td>5<\/td><td>$180^\\circ(5\\;-\\;2) = 540^\\circ$<\/td><td>$\\frac{540^\\circ}{5} = 108^\\circ$<\/td><\/tr><tr><td>Hexagon<\/td><td>6<\/td><td>$180^\\circ(6\\;-\\;2) = 720^\\circ$<\/td><td>$\\frac{720^\\circ}{6} = 120^\\circ$<\/td><\/tr><tr><td>Heptagon<\/td><td>7<\/td><td>$180^\\circ(7\\;-\\;2) = 900^\\circ$<\/td><td>$\\frac{900^\\circ}{7} = 128.57&#8230;^\\circ$<\/td><\/tr><tr><td>Octagon<\/td><td>8<\/td><td>$180^\\circ(8\\;-\\;2) = 1080^\\circ$<\/td><td>$\\frac{1080^\\circ}{8} = 135^\\circ$<\/td><\/tr><tr><td>Nonagon<\/td><td>9<\/td><td>$180^\\circ(9\\;-\\;2) = 1260^\\circ$<\/td><td>$\\frac{1260^\\circ}{9} = 140^\\circ$<\/td><\/tr><tr><td>Decagon<\/td><td>10<\/td><td>$180^\\circ(10\\;-\\;2) = 1440^\\circ$<\/td><td>$\\frac{1440^\\circ}{10} = 144^\\circ$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-facts-about-interior-angles\">Facts about Interior Angles<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If we intersect two straight lines, the opposite angles (vertically opposite angles) are equal. These angles have a common vertex and a common side.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">If any side of a triangle is extended, the exterior angle thus formed is equal to the sum of two remote interior angles. This is known as the Exterior Angle Theorem.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about interior angles, their types along with formulas. Now let us solve some examples and practice problems to understand the above concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"14-solved-examples-on-interior-angles\">Solved Examples on Interior Angles<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Five interior angles of an irregular hexagon are: <\/strong>$100^\\circ,\\; 130^\\circ,\\; 95^\\circ,\\; 125^\\circ$<strong> and <\/strong>$110^\\circ$<strong>. What is the value of its sixth angle?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the sum of angles of a hexagon is $720^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let the unknown angle be x.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$100^\\circ + 130^\\circ + 95^\\circ + 125^\\circ + 110^\\circ + x =720^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$560^\\circ + x = 720^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = 720^\\circ\\;-\\;560^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = 160^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the value of the unknown angle is $160^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. What is the sum of interior angles of a polygon with 15 sides?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The formula to calculate the sum of interior angles of any polygon with \u201cn\u201d sides is Sum=(n\u22122) \u00d7 180\u00b0<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Given, $n = 15$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$Sum = (15 \\;-\\; 2) \\times 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 13 \\times 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 2340^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the sum of interior angles of a polygon with 15 sides is $2340^\\circ$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. What will be the measure of each angle for a regular 15-gon?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the 15 sided polygon is regular, then the measure of each angle will be the total sum of all angles divided by the number of sides.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, measure of each angle $= \\frac{(n\\;\u2212\\;2)\\times180^\\circ}{n} = \\frac{2340}{15}=156^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the measure of each angle in a 15 sided regular polygon is $156^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. In the figure given below, if m<\/strong>$\\angle 1 = 105^\\circ$<strong>, what is the value m<\/strong>$\\angle 3$<strong>?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"253\" height=\"154\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/alternate-interior-angles-formed-by-a-transversal-and-two-parallel-lines.png\" alt=\"Alternate interior angles formed by a transversal and two parallel lines\" class=\"wp-image-32610\" title=\"Alternate interior angles formed by a transversal and two parallel lines\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">As we can see from the figure, $\\angle 1$ and $\\angle 3$ are alternate interior angles, By the property of alternate interior angles, these angles will be equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the measure of angle 3 will also be $105^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$m \\angle 3 = 105^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. In the figure given below, if <\/strong>$m\\angle 1 = 100^\\circ$<strong>, what will be the measure of:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>i) <\/strong>$4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>ii) <\/strong>$\\angle 3$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"253\" height=\"154\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/two-parallel-lines-and-a-transversal-forming-different-angles.png\" alt=\"Two parallel lines and a transversal forming different angles\" class=\"wp-image-32611\" title=\"Two parallel lines and a transversal forming different angles\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">i) As we can see from the figure, $\\angle 1$ and $\\angle 4$ are co-interior angles. The sum of co-interior angles is $180^\\circ$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let the measure of the angle 4 be x.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, we get the equation:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$100^\\circ + x = 180^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, x is equal to $80^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">ii) $\\angle 1$ and $\\angle 3$ are alternate interior angles. Thus, they are equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$m\\angle1 = m\\angle3 = 100^\\circ$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"15-practice-problems-on-interior-angles\">Practice Problems on Interior Angles<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Interior Angles - Definition, Theorem, Formula, Types, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">In an irregular pentagon, four of its angles are: $100^\\circ,\\; 90^\\circ,\\; 95^\\circ$ and $105^\\circ$. What is the measure of its fifth angle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$120^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$130^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$150^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$170^\\circ$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $150^\\circ$<br\/>We know that the sum of angles of a pentagon is $540^\\circ$.<br>\r\nLet the unknown angle be x.<br>\r\n$100^\\circ + 90^\\circ + 95^\\circ + 105^\\circ + x = 540^\\circ$<br>\r\n$390^\\circ + x = 540^\\circ$<br>\r\n$x = 540^\\circ\\;-\\;390^\\circ$<br>\r\n$x = 150^\\circ$<br>\r\nTherefore, the value of the unknown angle is $150^\\circ$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the sum of interior angles of a polygon with 12 sides?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1200<\/div><div class=\"spq_answer_block\" data-value=\"1\">1800<\/div><div class=\"spq_answer_block\" data-value=\"2\">1500<\/div><div class=\"spq_answer_block\" data-value=\"3\">2000<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1800<br\/>We know that the formula to calculate the sum of interior angles of any polygon with \u201cn\u201d sides is<br>\r\n$Sum = (n\\;\u2212\\;2)\\times180^\\circ$<br>\r\nHere, $n = 12$<br>\r\n$Sum = (12\\;-\\;2)\\times180^\\circ = 10\\times180^\\circ = 1800^\\circ$<br>\r\nTherefore, the sum of interior angles of a polygon with 12 sides is $1800^\\circ$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">In the above example, if the polygon is a regular polygon, what will be the measure of each angle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$150^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$120^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$90^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$135^\\circ$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $150^\\circ$<br\/>If the 12 sided polygon is regular, then the measure of each angle will be the total sum of all angles divided by the number of sides.<br>\r\nSo, $\\frac{1800^\\circ}{12} = 150^\\circ$.<br>\r\nHence, the measure of each angle in a 12 sided regular polygon is $150^\\circ$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">In the figure given below, if the measure of angle 1 is $120^\\circ$, what will be the measure of angle 3?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problems-5-1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$110^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$120^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$130^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$140^\\circ$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $120^\\circ$<br\/>As we can see from the figure, $\\angle1$ and $\\angle3$ are alternate interior angles. By the property of alternate interior angles, these angles will be equal.<br>\r\nTherefore,  $m\\angle3 = 120^\\circ$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Identify the pair of co-interior angles.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problems-4.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$\\angle1\\;and\\;\\angle2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\angle4\\;and\\;\\angle2$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\angle1\\;and\\;\\angle3$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\angle2\\;and\\;\\angle3$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\angle2\\;and\\;\\angle3$<br\/>$\\angle2$ and $\\angle3$ form a pair of co-interior angles. They lie on the same side of the transversal. Another pair of co-interior angles are: $\\angle1$ and $\\angle4$.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Interior Angles - Definition, Theorem, Formula, Types, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Interior Angles\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In an irregular pentagon, four of its angles are: $$100^\\\\circ,\\\\; 90^\\\\circ,\\\\; 95^\\\\circ$$ and $$105^\\\\circ$$. What is the measure of its fifth angle?\",\n                    \"text\": \"In an irregular pentagon, four of its angles are: $$100^\\\\circ,\\\\; 90^\\\\circ,\\\\; 95^\\\\circ$$ and $$105^\\\\circ$$. What is the measure of its fifth angle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that the sum of angles of a pentagon is $$540^\\\\circ$$.<br>\r\nLet the unknown angle be x.<br>\r\n$$100^\\\\circ + 90^\\\\circ + 95^\\\\circ + 105^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$390^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$x = 540^\\\\circ\\\\;-\\\\;390^\\\\circ$$<br>\r\n$$x = 150^\\\\circ$$<br>\r\nTherefore, the value of the unknown angle is $$150^\\\\circ$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$120^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the sum of angles of a pentagon is $$540^\\\\circ$$.<br>\r\nLet the unknown angle be x.<br>\r\n$$100^\\\\circ + 90^\\\\circ + 95^\\\\circ + 105^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$390^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$x = 540^\\\\circ\\\\;-\\\\;390^\\\\circ$$<br>\r\n$$x = 150^\\\\circ$$<br>\r\nTherefore, the value of the unknown angle is $$150^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$130^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the sum of angles of a pentagon is $$540^\\\\circ$$.<br>\r\nLet the unknown angle be x.<br>\r\n$$100^\\\\circ + 90^\\\\circ + 95^\\\\circ + 105^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$390^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$x = 540^\\\\circ\\\\;-\\\\;390^\\\\circ$$<br>\r\n$$x = 150^\\\\circ$$<br>\r\nTherefore, the value of the unknown angle is $$150^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$170^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the sum of angles of a pentagon is $$540^\\\\circ$$.<br>\r\nLet the unknown angle be x.<br>\r\n$$100^\\\\circ + 90^\\\\circ + 95^\\\\circ + 105^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$390^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$x = 540^\\\\circ\\\\;-\\\\;390^\\\\circ$$<br>\r\n$$x = 150^\\\\circ$$<br>\r\nTherefore, the value of the unknown angle is $$150^\\\\circ$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$150^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that the sum of angles of a pentagon is $$540^\\\\circ$$.<br>\r\nLet the unknown angle be x.<br>\r\n$$100^\\\\circ + 90^\\\\circ + 95^\\\\circ + 105^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$390^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$x = 540^\\\\circ\\\\;-\\\\;390^\\\\circ$$<br>\r\n$$x = 150^\\\\circ$$<br>\r\nTherefore, the value of the unknown angle is $$150^\\\\circ$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that the sum of angles of a pentagon is $$540^\\\\circ$$.<br>\r\nLet the unknown angle be x.<br>\r\n$$100^\\\\circ + 90^\\\\circ + 95^\\\\circ + 105^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$390^\\\\circ + x = 540^\\\\circ$$<br>\r\n$$x = 540^\\\\circ\\\\;-\\\\;390^\\\\circ$$<br>\r\n$$x = 150^\\\\circ$$<br>\r\nTherefore, the value of the unknown angle is $$150^\\\\circ$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the sum of interior angles of a polygon with 12 sides?\",\n                    \"text\": \"What is the sum of interior angles of a polygon with 12 sides?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that the formula to calculate the sum of interior angles of any polygon with \u201cn\u201d sides is<br>\r\n$$Sum = (n\\\\;\u2212\\\\;2)\\\\times180^\\\\circ$$<br>\r\nHere, $$n = 12$$<br>\r\n$$Sum = (12\\\\;-\\\\;2)\\\\times180^\\\\circ = 10\\\\times180^\\\\circ = 1800^\\\\circ$$<br>\r\nTherefore, the sum of interior angles of a polygon with 12 sides is $$1800^\\\\circ$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1200\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the formula to calculate the sum of interior angles of any polygon with \u201cn\u201d sides is<br>\r\n$$Sum = (n\\\\;\u2212\\\\;2)\\\\times180^\\\\circ$$<br>\r\nHere, $$n = 12$$<br>\r\n$$Sum = (12\\\\;-\\\\;2)\\\\times180^\\\\circ = 10\\\\times180^\\\\circ = 1800^\\\\circ$$<br>\r\nTherefore, the sum of interior angles of a polygon with 12 sides is $$1800^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1500\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the formula to calculate the sum of interior angles of any polygon with \u201cn\u201d sides is<br>\r\n$$Sum = (n\\\\;\u2212\\\\;2)\\\\times180^\\\\circ$$<br>\r\nHere, $$n = 12$$<br>\r\n$$Sum = (12\\\\;-\\\\;2)\\\\times180^\\\\circ = 10\\\\times180^\\\\circ = 1800^\\\\circ$$<br>\r\nTherefore, the sum of interior angles of a polygon with 12 sides is $$1800^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2000\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the formula to calculate the sum of interior angles of any polygon with \u201cn\u201d sides is<br>\r\n$$Sum = (n\\\\;\u2212\\\\;2)\\\\times180^\\\\circ$$<br>\r\nHere, $$n = 12$$<br>\r\n$$Sum = (12\\\\;-\\\\;2)\\\\times180^\\\\circ = 10\\\\times180^\\\\circ = 1800^\\\\circ$$<br>\r\nTherefore, the sum of interior angles of a polygon with 12 sides is $$1800^\\\\circ$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1800\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that the formula to calculate the sum of interior angles of any polygon with \u201cn\u201d sides is<br>\r\n$$Sum = (n\\\\;\u2212\\\\;2)\\\\times180^\\\\circ$$<br>\r\nHere, $$n = 12$$<br>\r\n$$Sum = (12\\\\;-\\\\;2)\\\\times180^\\\\circ = 10\\\\times180^\\\\circ = 1800^\\\\circ$$<br>\r\nTherefore, the sum of interior angles of a polygon with 12 sides is $$1800^\\\\circ$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that the formula to calculate the sum of interior angles of any polygon with \u201cn\u201d sides is<br>\r\n$$Sum = (n\\\\;\u2212\\\\;2)\\\\times180^\\\\circ$$<br>\r\nHere, $$n = 12$$<br>\r\n$$Sum = (12\\\\;-\\\\;2)\\\\times180^\\\\circ = 10\\\\times180^\\\\circ = 1800^\\\\circ$$<br>\r\nTherefore, the sum of interior angles of a polygon with 12 sides is $$1800^\\\\circ$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In the above example, if the polygon is a regular polygon, what will be the measure of each angle?\",\n                    \"text\": \"In the above example, if the polygon is a regular polygon, what will be the measure of each angle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If the 12 sided polygon is regular, then the measure of each angle will be the total sum of all angles divided by the number of sides.<br>\r\nSo, $$\\\\frac{1800^\\\\circ}{12} = 150^\\\\circ$$.<br>\r\nHence, the measure of each angle in a 12 sided regular polygon is $$150^\\\\circ$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$120^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the 12 sided polygon is regular, then the measure of each angle will be the total sum of all angles divided by the number of sides.<br>\r\nSo, $$\\\\frac{1800^\\\\circ}{12} = 150^\\\\circ$$.<br>\r\nHence, the measure of each angle in a 12 sided regular polygon is $$150^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$90^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the 12 sided polygon is regular, then the measure of each angle will be the total sum of all angles divided by the number of sides.<br>\r\nSo, $$\\\\frac{1800^\\\\circ}{12} = 150^\\\\circ$$.<br>\r\nHence, the measure of each angle in a 12 sided regular polygon is $$150^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$135^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the 12 sided polygon is regular, then the measure of each angle will be the total sum of all angles divided by the number of sides.<br>\r\nSo, $$\\\\frac{1800^\\\\circ}{12} = 150^\\\\circ$$.<br>\r\nHence, the measure of each angle in a 12 sided regular polygon is $$150^\\\\circ$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$150^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If the 12 sided polygon is regular, then the measure of each angle will be the total sum of all angles divided by the number of sides.<br>\r\nSo, $$\\\\frac{1800^\\\\circ}{12} = 150^\\\\circ$$.<br>\r\nHence, the measure of each angle in a 12 sided regular polygon is $$150^\\\\circ$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If the 12 sided polygon is regular, then the measure of each angle will be the total sum of all angles divided by the number of sides.<br>\r\nSo, $$\\\\frac{1800^\\\\circ}{12} = 150^\\\\circ$$.<br>\r\nHence, the measure of each angle in a 12 sided regular polygon is $$150^\\\\circ$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In the figure given below, if the measure of angle 1 is $$120^\\\\circ$$, what will be the measure of angle 3?\",\n                    \"text\": \"In the figure given below, if the measure of angle 1 is $$120^\\\\circ$$, what will be the measure of angle 3? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problems-5-1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"As we can see from the figure, $$\\\\angle1$$ and $$\\\\angle3$$ are alternate interior angles. By the property of alternate interior angles, these angles will be equal.<br>\r\nTherefore,  $$m\\\\angle3 = 120^\\\\circ$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$110^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"As we can see from the figure, $$\\\\angle1$$ and $$\\\\angle3$$ are alternate interior angles. By the property of alternate interior angles, these angles will be equal.<br>\r\nTherefore,  $$m\\\\angle3 = 120^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$130^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"As we can see from the figure, $$\\\\angle1$$ and $$\\\\angle3$$ are alternate interior angles. By the property of alternate interior angles, these angles will be equal.<br>\r\nTherefore,  $$m\\\\angle3 = 120^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$140^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"As we can see from the figure, $$\\\\angle1$$ and $$\\\\angle3$$ are alternate interior angles. By the property of alternate interior angles, these angles will be equal.<br>\r\nTherefore,  $$m\\\\angle3 = 120^\\\\circ$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$120^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"As we can see from the figure, $$\\\\angle1$$ and $$\\\\angle3$$ are alternate interior angles. By the property of alternate interior angles, these angles will be equal.<br>\r\nTherefore,  $$m\\\\angle3 = 120^\\\\circ$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"As we can see from the figure, $$\\\\angle1$$ and $$\\\\angle3$$ are alternate interior angles. By the property of alternate interior angles, these angles will be equal.<br>\r\nTherefore,  $$m\\\\angle3 = 120^\\\\circ$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the pair of co-interior angles.\",\n                    \"text\": \"Identify the pair of co-interior angles. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problems-4.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\angle2$$ and $$\\\\angle3$$ form a pair of co-interior angles. They lie on the same side of the transversal. Another pair of co-interior angles are: $$\\\\angle1$$ and $$\\\\angle4$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\angle1\\\\;and\\\\;\\\\angle2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\angle2$$ and $$\\\\angle3$$ form a pair of co-interior angles. They lie on the same side of the transversal. Another pair of co-interior angles are: $$\\\\angle1$$ and $$\\\\angle4$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\angle4\\\\;and\\\\;\\\\angle2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\angle2$$ and $$\\\\angle3$$ form a pair of co-interior angles. They lie on the same side of the transversal. Another pair of co-interior angles are: $$\\\\angle1$$ and $$\\\\angle4$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\angle1\\\\;and\\\\;\\\\angle3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\angle2$$ and $$\\\\angle3$$ form a pair of co-interior angles. They lie on the same side of the transversal. Another pair of co-interior angles are: $$\\\\angle1$$ and $$\\\\angle4$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\angle2\\\\;and\\\\;\\\\angle3$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\angle2$$ and $$\\\\angle3$$ form a pair of co-interior angles. They lie on the same side of the transversal. Another pair of co-interior angles are: $$\\\\angle1$$ and $$\\\\angle4$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\angle2$$ and $$\\\\angle3$$ form a pair of co-interior angles. They lie on the same side of the transversal. Another pair of co-interior angles are: $$\\\\angle1$$ and $$\\\\angle4$$.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"16-frequently-asked-questions-on-interior-angles\">Frequently Asked Questions on Interior Angles<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-c675ac77-e174-4c97-9924-2f72b62981e9\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-c675ac77-e174-4c97-9924-2f72b62981e9\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c675ac77-e174-4c97-9924-2f72b62981e9\"><strong>What are the types of triangles based on the measure of interior angles?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-c675ac77-e174-4c97-9924-2f72b62981e9\">\n\n<p class=\"eplus-wrapper\">There are three types of angles based on the measure of interior angles.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Acute Triangles: All the three internal angles of the triangle are acute<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Obtuse Triangles: Any one of the angles is an obtuse angle (greater than $90^\\circ$).<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Right Triangles: One angle measures 90 degrees.<\/li>\n<\/ul>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-c675ac77-e174-4c97-9924-2f72b62981e9\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c675ac77-e174-4c97-9924-2f72b62981e9\"><strong>What are the parts of an angle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-c675ac77-e174-4c97-9924-2f72b62981e9\">\n\n<p class=\"eplus-wrapper\">Vertex: The corner point where the arms meet.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Arms: Two rays that meet to form an angle.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-c675ac77-e174-4c97-9924-2f72b62981e9\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c675ac77-e174-4c97-9924-2f72b62981e9\"><strong>What are acute angles?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-c675ac77-e174-4c97-9924-2f72b62981e9\">\n\n<p class=\"eplus-wrapper\">Angles that are between $0^\\circ$ and $90^\\circ$ are known as acute angles.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-c675ac77-e174-4c97-9924-2f72b62981e9\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c675ac77-e174-4c97-9924-2f72b62981e9\"><strong>What are obtuse angles?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-c675ac77-e174-4c97-9924-2f72b62981e9\">\n\n<p class=\"eplus-wrapper\">Angles that are greater than $90^\\circ$ but less than $180^\\circ$ are known as obtuse angles.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-c675ac77-e174-4c97-9924-2f72b62981e9\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c675ac77-e174-4c97-9924-2f72b62981e9\"><strong>What are supplementary angles?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-c675ac77-e174-4c97-9924-2f72b62981e9\">\n\n<p class=\"eplus-wrapper\">When the sum of two angles is $180^\\circ$, each of the two angles are called supplementary angles.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-c675ac77-e174-4c97-9924-2f72b62981e9\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-c675ac77-e174-4c97-9924-2f72b62981e9\"><strong>What is the interior of an angle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-c675ac77-e174-4c97-9924-2f72b62981e9\">\n\n<p class=\"eplus-wrapper\">Interior of an angle definition in geometry: It is the region or area between the two rays that form the angle. It extends indefinitely from the vertex to infinity.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Interior Angles? The term \u201cinterior angles\u201d in geometry can be used in two different contexts. Let\u2019s explore the meaning of interior angles with respect to each of these cases along with types, different formulas and examples. Interior Angles Definition Interior Angles Formed When Two Parallel Lines Are Cut By a Transversal The angles &#8230; <a title=\"Interior Angles &#8211; Definition, Theorem, Formula, Types, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles\" aria-label=\"More on Interior Angles &#8211; Definition, Theorem, Formula, Types, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-27926","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27926","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=27926"}],"version-history":[{"count":57,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27926\/revisions"}],"predecessor-version":[{"id":39886,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27926\/revisions\/39886"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27926"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27926"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27926"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}