{"id":30757,"date":"2023-06-18T09:43:52","date_gmt":"2023-06-18T09:43:52","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=30757"},"modified":"2023-11-15T17:48:44","modified_gmt":"2023-11-15T17:48:44","slug":"angles-in-a-quadrilateral-definition-properties-examples-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/angles-in-a-quadrilateral","title":{"rendered":"Angles in a Quadrilateral &#8211; Definition, Properties, Examples, Facts"},"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-407e77e6-0488-430c-898a-e1f78c56ee8d\" 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\/angles-in-a-quadrilateral#0-what-are-angles-in-a-quadrilateral>What Are Angles in a Quadrilateral?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angles-in-a-quadrilateral#1-interior-angles-and-exterior-angles-of-a-quadrilateral>Interior Angles and Exterior Angles of a Quadrilateral<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angles-in-a-quadrilateral#3-how-to-find-the-missing-angle-in-a-quadrilateral>How to Find the Missing Angle in a Quadrilateral<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angles-in-a-quadrilateral#8-solved-examples-on-angles-in-a-quadrilateral>Solved Examples on Angles in a Quadrilateral<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angles-in-a-quadrilateral#9-practice-problems-on-angles-in-a-quadrilateral>Practice Problems on Angles in a Quadrilateral<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angles-in-a-quadrilateral#10-frequently-asked-questions-on-angles-in-a-quadrilateral>Frequently Asked Questions on Angles in a Quadrilateral<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-angles-in-a-quadrilateral\">What Are Angles in a Quadrilateral?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/angle\"><strong>Angles<\/strong><\/a><strong> in a <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/quadrilateral\"><strong>quadrilateral<\/strong><\/a><strong> are the four angles formed at each vertex. These angles are called interior angles of a quadrilateral.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you draw a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/diagonal\">diagonal<\/a>, you can see that a quadrilateral gets divided into two triangles. We know the sum of the interior angles of a triangle is 180\u00b0. It follows that the sum of angles in a quadrilateral is 360\u00b0.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"313\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/sum-of-angles-in-a-quadrilateral-is-360-degrees-visual-proof.png\" alt=\"Sum of angles in a quadrilateral is 360 degrees: visual proof\" class=\"wp-image-35935\" title=\"Sum of angles in a quadrilateral is 360 degrees: visual proof\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/sum-of-angles-in-a-quadrilateral-is-360-degrees-visual-proof.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/sum-of-angles-in-a-quadrilateral-is-360-degrees-visual-proof-300x151.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four interior angles. A quadrilateral is a four-sided <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\">polygon<\/a> shape formed by four non-collinear points.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"395\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/4-non-collinear-points-forming-a-quadrilateral.png\" alt=\"4 non-collinear points forming a quadrilateral\" class=\"wp-image-35937\" title=\"4 non-collinear points forming a quadrilateral\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/4-non-collinear-points-forming-a-quadrilateral.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/4-non-collinear-points-forming-a-quadrilateral-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In the figure given above, ABCD is a quadrilateral.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AB, BC, CD, and DA are four sides of the quadrilateral.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A, B, C, and D are four vertices.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\angle A, \\angle B, \\angle C$, and $\\angle D$ are the four interior angles of this quadrilateral.<\/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-quadrilaterals-in-different-orientation\" 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_rhombus_parallelogram_orientation_pt.png\" alt=\"Classify Quadrilaterals in Different Orientation 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 Quadrilaterals in Different Orientation 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-quadrilaterals\" 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_3_pt.png\" alt=\"Find the Perimeter of the Quadrilaterals 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 Quadrilaterals 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            }\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\" id=\"1-interior-angles-and-exterior-angles-of-a-quadrilateral\">Interior Angles and Exterior Angles of a Quadrilateral<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">There are 4 interior angles and 4 exterior angles in a quadrilateral.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s understand the difference between the interior and exterior angles of a quadrilateral.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Interior Angles of a Quadrilateral<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The sum of the interior angles of a quadrilateral is $360^{\\circ}$. If there is one missing angle, we can use this property to find the measure of the missing angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Exterior Angles of a Quadrilateral<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An exterior angle is formed by the intersection of any of the sides of a polygon and extension of the adjacent side. The sum of all the exterior angles of a quadrilateral is $360^{\\circ}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Take a look at the quadrilateral ABCD. Angles 1, 2, 3, and 4 are the exterior angles. Angles A, B, C, and D are <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles\">interior angles<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"366\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/exterior-angles-of-a-quadrilateral-is-180-degrees.png\" alt=\"Exterior angles of a quadrilateral is 180 degrees\" class=\"wp-image-35938\" title=\"Exterior angles of a quadrilateral is 180 degrees\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/exterior-angles-of-a-quadrilateral-is-180-degrees.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/exterior-angles-of-a-quadrilateral-is-180-degrees-300x177.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">$\\text{Interior Angle} + \\text{Corresponding Exterior Angle} = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\angle A + \\angle 1 = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\angle B + \\angle 2 = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\angle C + \\angle 3 = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\angle D + \\angle 4 = 180^{\\circ}$<\/p>\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\" id=\"2-angles-of-a-quadrilateral-formulas\">Angles of a Quadrilateral Formulas<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s take a look at some basic formulas related to the interior and exterior angles of a quadrilateral.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Interior Angles Sum Property<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The sum of interior angles of a polygon $= Sum = (n \\;-\\; 2) \\times 180^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where \u201cn\u201d is the number of sides of the given polygon.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In a quadrilateral, $n = 4$.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sum of interior angles of a quadrilateral $= (4 \\;\u2212\\; 2) 180^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Sum of interior angles of a quadrilateral <\/strong>$= 360^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Note:<\/strong> If 3 angles of a quadrilateral are known, then the 4th angle can be calculated using the formula:<strong> <\/strong>$360^{\\circ} \\;-\\;$ (Sum of the other 3 interior angles)<strong>.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Interior angle and corresponding exterior angle<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The sum of an interior angle and its corresponding exterior angle is always 180.<strong>&nbsp;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Exterior angle $= 180^{\\circ} \\;-\\;$ Corresponding Interior angle<\/li>\n\n\n\n<li>Interior angle $=&nbsp; 180^{\\circ} \\;-\\;$ Corresponding Exterior angle<strong>&nbsp;<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Exterior Angles Sum of a Quadrilateral<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The sum of exterior angles of a quadrilateral is $360^{\\circ}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let angles W, X, Y, Z be the exterior angles corresponding to the interior angles A, B, C, D of a quadrilateral respectively.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, $W + X + Y + Z = (180^{\\circ} \\;-\\; A) + &nbsp;(180^{\\circ} \\;-\\; B) +&nbsp; (180^{\\circ} \\;-\\; C) +&nbsp; (180^{\\circ} \\;-\\; D)$&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$W + X + Y + Z = (180^{\\circ} + 180^{\\circ} + 180^{\\circ} + 180^{\\circ}) \\;-\\; (A + B + C + D)$&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$W + X + Y + Z = (180^{\\circ} + 180^{\\circ} + 180^{\\circ} + 180^{\\circ}) \\;-\\;&nbsp; 360^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(\u2026interior angles of a quadrilateral add up to $360^{\\circ}$.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$W + X + Y + Z = 360^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, sum of exterior angles of a quadrilateral $= 360^{\\circ}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"520\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/Interior-and-exterior-angles-of-a-quadrilateral.png\" alt=\"Interior and exterior angles of a quadrilateral\" class=\"wp-image-35939\" title=\"Interior and exterior angles of a quadrilateral\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/Interior-and-exterior-angles-of-a-quadrilateral.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/Interior-and-exterior-angles-of-a-quadrilateral-300x252.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-find-the-missing-angle-in-a-quadrilateral\">How to Find the Missing Angle in a Quadrilateral<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 1:<\/strong> Use angle properties to determine interior angles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 2:<\/strong> Add all known interior angles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Step 3:<\/strong> Subtract the angle sum from $360^{\\circ}$.<br><br><strong>Example: <\/strong>Find the missing angle in the quadrilateral given below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/angle-measures-in-a-quadrilateral.png\" alt=\"Angle measures in a quadrilateral\" class=\"wp-image-35940\" title=\"Angle measures in a quadrilateral\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/angle-measures-in-a-quadrilateral.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/angle-measures-in-a-quadrilateral-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">We know that the sum of the interior angles of a quadrilateral is $360^{\\circ}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Adding the given 3 angles, we get<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$100^{\\circ} + 95^{\\circ} + 60^{\\circ} = 255^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Subtracting the sum from $360^{\\circ}$, we get&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$360^{\\circ} \\;-\\; 255^{\\circ} = x$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus,&nbsp; $x = 105$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-properties-of-angles-in-a-quadrilateral\">Properties of Angles in a Quadrilateral<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let us look at the angle properties of a few common quadrilaterals.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rectangle\"><strong>Rectangle<\/strong><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"340\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rectangle-PQRS.png\" alt=\"Rectangle PQRS\" class=\"wp-image-35941\" title=\"Rectangle PQRS\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rectangle-PQRS.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rectangle-PQRS-300x165.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>All interior angles measure $90^{\\circ}$.<\/li>\n\n\n\n<li>Diagonals bisect each other and form four angles at the point of intersection, two acute angles and two obtuse angles.<\/li>\n\n\n\n<li>The diagonals do not bisect the angles at vertices.<\/li>\n\n\n\n<li>Vertically opposite angles at the intersection of the diagonals.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallelogram\"><strong>Parallelogram<\/strong><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"427\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/parallelogram-ABCD.png\" alt=\"Parallelogram ABCD\" class=\"wp-image-35942\" title=\"Parallelogram ABCD\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/parallelogram-ABCD.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/parallelogram-ABCD-300x207.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Opposite angles are equal.<\/li>\n\n\n\n<li>Adjacent angles or consecutive angles are supplementary.<\/li>\n\n\n\n<li>Vertically opposite angles are formed at the intersection of the diagonals.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/square\"><strong>Square<\/strong><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"334\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/square-PQRS.png\" alt=\"Square PQRS\" class=\"wp-image-35943\" title=\"Square PQRS\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/square-PQRS.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/square-PQRS-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>All interior angles are congruent and measure $90^{\\circ}$.<\/li>\n\n\n\n<li>Diagonals bisect each other at right angles.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rhombus\"><strong>Rhombus<\/strong><\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"350\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rhombus-PQRS.png\" alt=\"Rhombus PQRS\" class=\"wp-image-35944\" title=\"Rhombus PQRS\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rhombus-PQRS.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rhombus-PQRS-300x169.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Opposite angles are the equal.<\/li>\n\n\n\n<li>Adjacent angles are supplementary.<\/li>\n\n\n\n<li>Diagonals of a rhombus bisect each other at right angles.<\/li>\n\n\n\n<li>Diagonals of a rhombus bisect vertex angles.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Quadrilateral Family<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Take a look at the different types of quadrilaterals shown below. You can make an anchor chart to explore different properties of angles and sides in each of the given quadrilaterals &amp; their types. Try it out!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"778\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/quadrilateral-familya.png\" alt=\"Quadrilateral familya\" class=\"wp-image-35945\" title=\"Quadrilateral family\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/quadrilateral-familya.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/quadrilateral-familya-239x300.png 239w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-angles-of-a-quadrilateral-inscribed-in-a-circle\">Angles of a Quadrilateral Inscribed in a Circle<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"345\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/cyclic-quadrilaterals.png\" alt=\"Cyclic quadrilaterals\" class=\"wp-image-35946\" title=\"Cyclic quadrilaterals\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/cyclic-quadrilaterals.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/cyclic-quadrilaterals-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">When a quadrilateral is inscribed in a circle, it is known as a cyclic quadrilateral or a chordal quadrilateral. It is a quadrilateral that has all its four vertices lying on the circumference of a circle. In a cyclic quadrilateral, the four sides of the quadrilateral form the chords of the circle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The sum of opposite angles in a cyclic quadrilateral is <\/strong>$180^{\\circ}$<strong>. In other words, opposite angles in a cyclic quadrilateral are supplementary.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"618\" height=\"344\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/opposite-angles-in-a-cyclic-quadrilateral-are-supplementary.png\" alt=\"Opposite angles in a cyclic quadrilateral are supplementary\" class=\"wp-image-35947\" title=\"Opposite angles in a cyclic quadrilateral are supplementary\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/opposite-angles-in-a-cyclic-quadrilateral-are-supplementary.png 618w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/opposite-angles-in-a-cyclic-quadrilateral-are-supplementary-300x167.png 300w\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-facts-about-angles-in-a-quadrilateral\">Facts about Angles in a Quadrilateral<\/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-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Angles in a quadrilateral add up to $360^{\\circ}$.<\/li>\n\n\n\n<li>Any quadrilateral with four right angles is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/rectangle\">rectangle<\/a>.<\/li>\n\n\n\n<li>A quadrilateral with four right angles and four equal sides is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/square\">square<\/a>.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we learned about the angles of a quadrilateral, its properties, interior and exterior angles, angles of a quadrilateral inscribed in a circle and some important formulas. Let us apply those formulas to solve some examples!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-examples-on-angles-in-a-quadrilateral\">Solved Examples on Angles in a Quadrilateral<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. The angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4. Find the measure of each angle.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The given angle ratio is 1 : 2 : 3 : 4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let the measures of the four angles be $x,\\; 2x,\\; 3x$, and&nbsp; $4x$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The sum of interior angles of a quadrilateral is $360^{\\circ}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$x + 2x +&nbsp; 3x + 4x = 360^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$10 x = 360^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$x = 36^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the measure of four angles are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$x = 36^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$2x = 2(36^{\\circ}) = 72^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$3x = 3(36^{\\circ}) = 108^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$4x = 4(36^{\\circ}) = 144^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the angles of a quadrilateral are $36^{\\circ},\\;72^{\\circ},\\; 108^{\\circ}$ and $144^{\\circ}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Find the exterior angle of a quadrilateral whose corresponding interior angle is <\/strong>$60^{\\circ}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We know that the interior and exterior angles of a quadrilateral form a linear pair.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, using the formula for the exterior angle of a quadrilateral,&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exterior angle $= 180^{\\circ}\\;-\\;$ Interior angle<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exterior angle $= 180^{\\circ} \\;-\\;&nbsp; 60^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 120^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The exterior angle of the quadrilateral is $120^{\\circ}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Find the corresponding interior angle of a quadrilateral if its exterior angle is <\/strong>$104^{\\circ}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We know that the interior angle and the corresponding exterior angle of a quadrilateral form a linear pair.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, using the formula for the exterior angle of a quadrilateral.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exterior angle $= 180^{\\circ} \\;-\\;$ Interior angle<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Interior angle $= 180^{\\circ} \\;-\\;$&nbsp; Exterior angle&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Interior angle $= 180^{\\circ} \\;-\\; 104$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Interior angle $= 76^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The corresponding interior angle of the quadrilateral is $76^{\\circ}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. ABCD is a cyclic quadrilateral with center O. Find <\/strong><strong>x<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"296\" height=\"284\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/cyclic-quadrilateral.png\" alt=\"Cyclic quadrilateral\" class=\"wp-image-35948\" title=\"Cyclic quadrilateral\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">ABCD is a cyclic quadrilateral.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Opposite angles of a cyclic quadrilateral sum up to 180.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, $\\angle D + x = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$67^{\\circ} + x = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$x = 180^{\\circ} \\;-\\; 67^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$x = 113^{\\circ}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-angles-in-a-quadrilateral\">Practice Problems on Angles in a Quadrilateral<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Angles in a Quadrilateral - Definition, Properties, Examples, Facts<\/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\">Which of the following is not a quadrilateral?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Parallelogram<\/div><div class=\"spq_answer_block\" data-value=\"1\">Square<\/div><div class=\"spq_answer_block\" data-value=\"2\">Triangle<\/div><div class=\"spq_answer_block\" data-value=\"3\">Rhombus<\/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: Triangle<br\/>A triangle is not a quadrilateral as it has only three sides.<\/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 quadrilateral?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$180^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$160^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$90^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$270^{\\circ}$<\/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: $160^{\\circ}$<br\/>The interior angles of a quadrilateral always sum up to $360^{\\circ}$.<\/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\">Exterior angle and the corresponding interior angle of a quadrilateral add up to _______ angle.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$180^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$360^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$90^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$270^{\\circ}$<\/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: $180^{\\circ}$<br\/>Exterior angle and the corresponding interior angle of a quadrilateral form a $180^{\\circ}$ angle. <\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$100^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$20^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$110^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$290^{\\circ}$<\/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: $110^{\\circ}$<br\/>If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be, $180^{\\circ} \\;-\\; 70^{\\circ} = 110^{\\circ}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The sum of the opposite angles of a cyclic quadrilateral is _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$90^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$180^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$270^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$360^{\\circ}$<\/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: $180^{\\circ}$<br\/>The opposite angles in a cyclic quadrilateral are supplementary. The sum of the opposite angles is equal to $180^{\\circ}$.<\/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\": \"Angles in a Quadrilateral - Definition, Properties, Examples, Facts\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Angles in a Quadrilateral\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    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quadrilateral as it has only three sides.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Triangle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A triangle is not a quadrilateral as it has only three sides.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A triangle is not a quadrilateral as it has only three sides.\"\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 quadrilateral?\",\n                    \"text\": \"What is the sum of interior angles of a quadrilateral?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The interior angles of a quadrilateral always sum up to $$360^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$180^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The interior angles of a quadrilateral always sum up to $$360^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$90^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The interior angles of a quadrilateral always sum up to $$360^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$270^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The interior angles of a quadrilateral always sum up to $$360^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$160^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The interior angles of a quadrilateral always sum up to $$360^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The interior angles of a quadrilateral always sum up to $$360^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Exterior angle and the corresponding interior angle of a quadrilateral add up to _______ angle.\",\n                    \"text\": \"Exterior angle and the corresponding interior angle of a quadrilateral add up to _______ angle.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Exterior angle and the corresponding interior angle of a quadrilateral form a $$180^{\\\\circ}$$ angle. \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$360^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Exterior angle and the corresponding interior angle of a quadrilateral form a $$180^{\\\\circ}$$ angle. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$90^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Exterior angle and the corresponding interior angle of a quadrilateral form a $$180^{\\\\circ}$$ angle. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$270^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Exterior angle and the corresponding interior angle of a quadrilateral form a $$180^{\\\\circ}$$ angle. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$180^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Exterior angle and the corresponding interior angle of a quadrilateral form a $$180^{\\\\circ}$$ angle. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Exterior angle and the corresponding interior angle of a quadrilateral form a $$180^{\\\\circ}$$ angle. \"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be _______.\",\n                    \"text\": \"If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be, $$180^{\\\\circ} \\\\;-\\\\; 70^{\\\\circ} = 110^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$100^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be, $$180^{\\\\circ} \\\\;-\\\\; 70^{\\\\circ} = 110^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$20^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be, $$180^{\\\\circ} \\\\;-\\\\; 70^{\\\\circ} = 110^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$290^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be, $$180^{\\\\circ} \\\\;-\\\\; 70^{\\\\circ} = 110^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$110^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be, $$180^{\\\\circ} \\\\;-\\\\; 70^{\\\\circ} = 110^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If an interior angle of a quadrilateral is 70, then its corresponding exterior angle will be, $$180^{\\\\circ} \\\\;-\\\\; 70^{\\\\circ} = 110^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The sum of the opposite angles of a cyclic quadrilateral is _______.\",\n                    \"text\": \"The sum of the opposite angles of a cyclic quadrilateral is _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. The sum of the opposite angles is equal to $$180^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$90^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. The sum of the opposite angles is equal to $$180^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$270^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. The sum of the opposite angles is equal to $$180^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$360^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. The sum of the opposite angles is equal to $$180^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$180^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. The sum of the opposite angles is equal to $$180^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The opposite angles in a cyclic quadrilateral are supplementary. The sum of the opposite angles is equal to $$180^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-on-angles-in-a-quadrilateral\">Frequently Asked Questions on Angles in a Quadrilateral<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-79fb89d8-62e6-4612-bbb8-bf380db83df1\" 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-0-79fb89d8-62e6-4612-bbb8-bf380db83df1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-79fb89d8-62e6-4612-bbb8-bf380db83df1\"><strong>Can all the angles of a quadrilateral be 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-0-79fb89d8-62e6-4612-bbb8-bf380db83df1\">\n\n<p class=\"wp-block-paragraph\">No, all angles of a quadrilateral cannot be acute angles. <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/acute-angle\">Acute angles<\/a> are the angles less than $90^{\\circ}$. If all the angles in a quadrilateral be less than $90^{\\circ}$, the sum of interior angles will never be $360^{\\circ}$. All angles of quadrilateral can be $90^{\\circ}$, which will form a rectangle (or a square) but not less than $90^{\\circ}$.<\/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-1-79fb89d8-62e6-4612-bbb8-bf380db83df1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-79fb89d8-62e6-4612-bbb8-bf380db83df1\"><strong>Is a triangle a quadrilateral?<\/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-1-79fb89d8-62e6-4612-bbb8-bf380db83df1\">\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">Triangles<\/a> are polygons with three sides. Quadrilaterals are polygons with four sides. A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. Therefore, even though a triangle is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/polygon\">polygon<\/a>, it is not a quadrilateral.<\/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-2-79fb89d8-62e6-4612-bbb8-bf380db83df1\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-79fb89d8-62e6-4612-bbb8-bf380db83df1\"><strong>What are the adjacent angles and opposite angles in a quadrilateral?<\/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-2-79fb89d8-62e6-4612-bbb8-bf380db83df1\">\n\n<p class=\"wp-block-paragraph\">Two angles of a quadrilateral having a common arm are called adjacent angles.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The opposite angles do not share a common arm. They lie diagonally opposite to each other.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"373\" height=\"251\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/06\/angles-of-quadrilateral-FAQ1.png\" alt=\"Adjacent and opposite angles in a quadrilateral\" class=\"wp-image-30777\" title=\"Adjacent and opposite angles in a quadrilateral\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/06\/angles-of-quadrilateral-FAQ1.png 373w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/06\/angles-of-quadrilateral-FAQ1-300x202.png 300w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><\/figure>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Angles in a Quadrilateral? Angles in a quadrilateral are the four angles formed at each vertex. These angles are called interior angles of a quadrilateral.&nbsp; If you draw a diagonal, you can see that a quadrilateral gets divided into two triangles. We know the sum of the interior angles of a triangle is &#8230; <a title=\"Angles in a Quadrilateral &#8211; Definition, Properties, Examples, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/angles-in-a-quadrilateral\" aria-label=\"More on Angles in a Quadrilateral &#8211; Definition, Properties, Examples, Facts\">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-30757","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\/30757","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=30757"}],"version-history":[{"count":13,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/30757\/revisions"}],"predecessor-version":[{"id":35949,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/30757\/revisions\/35949"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=30757"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=30757"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=30757"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}