{"id":31709,"date":"2023-07-11T16:12:00","date_gmt":"2023-07-11T16:12:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=31709"},"modified":"2023-07-12T05:54:35","modified_gmt":"2023-07-12T05:54:35","slug":"alternate-angles-definition-types-theorem-examples-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-angles","title":{"rendered":"Alternate Angles: Definition, Types, Theorem, 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-590617e1-637e-45a7-a29d-b554e93db3ce\" 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\/alternate-angles#0-what-are-alternate-angles>What Are Alternate Angles?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-angles#3-alternate-interior-angles-theorem>Alternate Interior Angles Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-angles#4-alternate-exterior-angles-theorem>Alternate Exterior Angles Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-angles#8-solved-examples-on-alternate-angles>Solved Examples on Alternate Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-angles#9-practice-problems-on-alternate-angles>Practice Problems on Alternate Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-angles#10-frequently-asked-questions-about-alternate-angles>Frequently Asked Questions about Alternate Angles<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-alternate-angles\">What Are Alternate Angles?<\/h2>\n\n\n\n<p>When a transversal cuts a pair of <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-lines\">parallel lines<\/a> (or non-parallel lines), it forms different types of angles. Alternate interior angles are a set of non-adjacent angles on either side of the transversal.<\/p>\n\n\n\n<p>In each diagram given below, two parallel lines are cut by a transversal. All the angle pairs highlighted in the same color represent alternate angles. They are on alternate sides of the transversal. They don\u2019t have common vertices.<\/p>\n\n\n\n<p>Based on their position, they are further categorized as interior and exterior angles.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Diagram on the left: Alternate interior angles<\/li>\n\n\n\n<li>Diagram on the right: Alternate exterior angles<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"331\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/identifying-alternate-angles.png\" alt=\"Alternate angles\" class=\"wp-image-31714\" title=\"Alternate angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/identifying-alternate-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/identifying-alternate-angles-300x160.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Observe that we can quickly spot a pair of alternate interior angles using the Z-shape. Take a look at the positions of alternate interior angles.<\/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\/07\/alternate-angles.png\" alt=\"Alternate interior angles\" class=\"wp-image-31715\" title=\"Alternate interior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-angles-300x151.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Thus, alternate interior angles are also sometimes known as Z-angles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"419\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-interior-angles-in-Z-shape.png\" alt=\"Alternate angles are Z-shaped\" class=\"wp-image-31716\" title=\"Alternate angles are Z-shaped\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-interior-angles-in-Z-shape.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-interior-angles-in-Z-shape-300x203.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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            }\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-definition-of-alternate-angles\">Definition of Alternate Angles<\/h2>\n\n\n\n<p>Alternate angles are the non-adjacent angles that lie on the opposite sides of the transversal.&nbsp;&nbsp;<\/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-types-of-alternate-angles\">Types of Alternate Angles<\/h2>\n\n\n\n<p>There are two types of alternate angles based on their position with respect to the transversal and the parallel lines.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Alternate Interior Angles<\/li>\n\n\n\n<li>Alternate Exterior Angles&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s understand the two types of alternate angles and their properties.<\/p>\n\n\n\n<p><strong>Alternate Interior Angles<\/strong><\/p>\n\n\n\n<p>The pair of angles that lie on the inner side (or the interior region) of the two parallel lines, but on the opposite sides of the transversal are known as alternate interior angles.&nbsp;<\/p>\n\n\n\n<p>So, what do alternate interior angles look like? In the image given below, the angle-pairs highlighted in the same color represent the alternate interior angles.<\/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\/07\/alternate-interior-angles.png\" alt=\"Alternate interior angles\" class=\"wp-image-31717\" title=\"Alternate interior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-interior-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-interior-angles-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>In the above image, the alternate interior angles are<\/p>\n\n\n\n<p>$\\angle 4$ and $\\angle 5$<\/p>\n\n\n\n<p>$\\angle 3$ and $\\angle 6$<\/p>\n\n\n\n<p><strong>Alternate Exterior Angles<\/strong><\/p>\n\n\n\n<p>The pair of angles that lie on the outside region of the two parallel lines, but on the opposite sides of the transversal are known as alternate exterior angles.&nbsp;<\/p>\n\n\n\n<p>The angle-pairs highlighted in the same color represent the alternate exterior angles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-exterior-angles.png\" alt=\"Alternate exterior angles\" class=\"wp-image-31718\" title=\"Alternate exterior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-exterior-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-exterior-angles-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>In the above image, the alternate exterior angles are<\/p>\n\n\n\n<p>$\\angle 1$ and $\\angle 8$<\/p>\n\n\n\n<p>$\\angle 2$ and $\\angle 7$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-alternate-interior-angles-theorem\">Alternate Interior Angles Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-5f86cfe3-9e88-4f7b-98ab-4f8c0762d664\">\n\n\n<p><strong>Alternate Angles Theorem Statement:<\/strong> If two parallel lines are cut by a transversal, then the pairs of alternate interior angles formed are congruent.<\/p>\n\n\n\n<p><strong>Converse: <\/strong>If two lines are cut by a transversal such that the alternate interior angles are congruent, then the lines are parallel.<\/p>\n\n\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"4-alternate-exterior-angles-theorem\">Alternate Exterior Angles Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-0e7ec207-9284-4acd-9a49-349923e07b17\">\n\n\n<p><strong>Alternate Exterior Angles Theorem Statement:<\/strong> If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles formed are congruent.<\/p>\n\n\n\n<p><strong>Converse: <\/strong>If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel.<\/p>\n\n\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"5-alternate-angles-theorem-proof\">Alternate Angles Theorem Proof<\/h2>\n\n\n\n<p>Assume that PQ and RS are the two parallel lines cut by a transversal LM.&nbsp;<\/p>\n\n\n\n<p>a, b, c, d are the angles created by the transversal.<\/p>\n\n\n\n<p>Since the corresponding angles are congruent, we have a corresponding pair for each of these angles, which are also labeled as a, b, c, and d.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"425\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/parallel-lines-and-transversal.png\" alt=\"Interior and Exterior Angles\" class=\"wp-image-31719\" title=\"Interior and Exterior Angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/parallel-lines-and-transversal.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/parallel-lines-and-transversal-300x205.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p>At the intersection point on the lines t and l,<\/p>\n\n\n\n<p>$\\angle a + \\angle d = 180^{\\circ}$ ( PQ is the straight line)\u2014\u00a0 (1)<\/p>\n\n\n\n<p>$\\angle b + \\angle d = 180^{\\circ}$ ( LM is the straight line)\u2014\u00a0 (2)<\/p>\n\n\n\n<p>So, from (1) and (2), we get<\/p>\n\n\n\n<p>$\\angle a = \\angle b$<\/p>\n\n\n\n<p>Again, at the intersection point on the straight lines LM and RS,<\/p>\n\n\n\n<p>$\\angle a + \\angle d = 180^{\\circ}$ ( RS is the straight line)\u2014 (3)<\/p>\n\n\n\n<p>$\\angle a + \\angle c = 180^{\\circ}$ ( LM is the straight line)\u2014\u00a0 (4)<\/p>\n\n\n\n<p>So, from (3) and (4), we get<\/p>\n\n\n\n<p>$\\angle d = \\angle c$<\/p>\n\n\n\n<p>Therefore, it is concluded that the alternate interior angles are congruent.<\/p>\n\n\n\n<p>Hence, proved.<\/p>\n\n\n\n<p><strong>Another way:<\/strong><\/p>\n\n\n\n<p>Here, we use the fact that the corresponding angles formed when a transversal cuts a pair of parallel lines are congruent.<\/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\/07\/parallel-lines-cut-by-transversal.png\" alt=\"Parallel lines m and n cut by a transversal t\" class=\"wp-image-31720\" title=\"Parallel lines m and n cut by a transversal t\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/parallel-lines-cut-by-transversal.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/parallel-lines-cut-by-transversal-300x177.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Here, $\\angle 1 = \\angle 5$ \u2026corresponding angles<\/p>\n\n\n\n<p>$\\angle 1 = \\angle 4$ \u2026opposite angles<\/p>\n\n\n\n<p>Thus, $\\angle 4 = \\angle 5$\u00a0 \u2026alternate interior angles<\/p>\n\n\n\n<p>Also, $\\angle 1 = \\angle 4$ \u2026opposite angles<\/p>\n\n\n\n<p>$\\angle 4 = \\angle 8$ \u2026corresponding angles<\/p>\n\n\n\n<p>Thus, $\\angle 1 = \\angle 8$ \u2026alternate exterior angles<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-facts-about-alternate-angles\">Facts about Alternate 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=\"wp-block-list\">\n<li>Alternate angles are angles that lie on opposite sides of the transversal line and have the same size.<\/li>\n\n\n\n<li>There are two different types of alternate angles, alternate interior angles and alternate exterior angles.<\/li>\n\n\n\n<li>The co-interior angles OR same-side interior angles add up to 180 degrees. The rule is sometimes remembered as \u201cC angles\u201d because the angles make a C shape.<\/li>\n\n\n\n<li>When two non-parallel lines intersect a transversal, the alternate interior angles formed will not be equal.<\/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>In this article, we learned about the alternate angles, types of alternate angles, and the theorems associated with it. Let\u2019s solve some examples and practice problems based on each of these concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-examples-on-alternate-angles\">Solved Examples on Alternate Angles<\/h2>\n\n\n\n<p><strong>1. Use the alternate interior angles theorem to determine if the lines cut by the transversal are parallel.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"254\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/interior-angles.png\" alt=\"Interior angles\" class=\"wp-image-31721\" title=\"Interior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/interior-angles.png 350w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/interior-angles-300x218.png 300w\" sizes=\"auto, (max-width: 350px) 100vw, 350px\" \/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Angle A and the angle measuring $60^{\\circ}$\u00a0form a straight angle.<\/p>\n\n\n\n<p>Thus, $m \\angle A + 60^{\\circ} = 180^{\\circ}$\u00a0<\/p>\n\n\n\n<p>$m \\angle A = 120^{\\circ}$<\/p>\n\n\n\n<p>Similarly, $\\angle B$ and $120^{\\circ}$ form a straight angle, so we know that\u00a0<\/p>\n\n\n\n<p>$m \\angle B + 120 = 180$<\/p>\n\n\n\n<p>$m \\angle B = 60^{\\circ}$<\/p>\n\n\n\n<p>$\\angle A$ and the original $120^{\\circ}$ angle are alternate interior angles and are equal.\u00a0<\/p>\n\n\n\n<p>$\\angle B$ and the original $60^{\\circ}$ angle are also equal alternate interior angles.\u00a0<\/p>\n\n\n\n<p>So, going by the <strong>alternate interior angles theorem<\/strong>, the lines cut by the transversal must be parallel.<\/p>\n\n\n\n<p><strong>2. In the diagram given below, the lines cut by the transversal are parallel. Determine the measures of the angles A, B, and C.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"350\" height=\"252\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/interior-angles-1.png\" alt=\"Interior angles\" class=\"wp-image-31722\" title=\"Interior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/interior-angles-1.png 350w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/interior-angles-1-300x216.png 300w\" sizes=\"auto, (max-width: 350px) 100vw, 350px\" \/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Angle A and 155 degrees are alternate interior angles, and so since the lines cut by the transversal are parallel, the measure of angle A is also 155 degrees.&nbsp;<\/p>\n\n\n\n<p>Angle A and angle B form a straight angle, so $A + B = 180^{\\circ}$.<\/p>\n\n\n\n<p>Since $A = 155^{\\circ},\\; 155^{\\circ} + B = 180^{\\circ}$.<\/p>\n\n\n\n<p>\u00a0$B = 25^{\\circ}$<\/p>\n\n\n\n<p>Thus the measure of angle B is $25^{\\circ}$.<\/p>\n\n\n\n<p>Now, since angle B and angle C are alternate interior angles, we know that the measure of angle C is also $25^{\\circ}$.<\/p>\n\n\n\n<p>Thus, the measures of $\\angle A,\\; \\angle B$ and $\\angle C$ are $155^{\\circ},\\; 25^{\\circ}$ and $25^{\\circ}$ respectively.<\/p>\n\n\n\n<p><strong>3. In the figure given below, CE is parallel to FH. Find the value of <\/strong><strong>x<\/strong><strong>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"323\" height=\"283\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-angles-question.png\" alt=\"Transversal intersecting two parallel lines\" class=\"wp-image-31723\" title=\"Transversal intersecting two parallel lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-angles-question.png 323w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-angles-question-300x263.png 300w\" sizes=\"auto, (max-width: 323px) 100vw, 323px\" \/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>In the given figure, $\\angle ADE$ and $\\angle FGJ$ form a pair of alternate exterior angles.<\/p>\n\n\n\n<p>By using alternate exterior angle theorem, we have, $\\angle ADE = \\angle FGJ$<\/p>\n\n\n\n<p>So, $x^{\\circ} + 50^{\\circ} = 130^{\\circ}$<\/p>\n\n\n\n<p>$x = 130^{\\circ} \\;-\\; 50^{\\circ}$<\/p>\n\n\n\n<p>$x = 80^{\\circ}$<\/p>\n\n\n\n<p>Therefore, the value of x is $80^{\\circ}$.<\/p>\n\n\n\n<p><strong>4. Calculate the value for <\/strong><strong>x&nbsp; <\/strong><strong>and find the value of each angle.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"293\" height=\"210\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-interior-angles-with-variables.png\" alt=\"Parallel lines cut by a transversal\" class=\"wp-image-31724\" title=\"Parallel lines cut by a transversal\"\/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Angles measuring $(6x \\;-\\; 10)$ and $(3x + 20)$ are alternate angles.<\/p>\n\n\n\n<p>We know that alternate angles are equal.<\/p>\n\n\n\n<p>\u00a0So, $6x \\;-\\; 10\u00a0 =\u00a0 3x + 20$<\/p>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0$6x \\;-\\; 3x = 20 + 10$<\/p>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0$3x\u00a0 = 30$<\/p>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0$x\u00a0 = 10$<\/p>\n\n\n\n<p>Substituting values in the equation of angles, we get,<\/p>\n\n\n\n<p>$6x \\;-\\; 10\u00a0 = 6 (10) \\;-\\; 10\u00a0 =\u00a0 60 \\;-\\; 10 = 50$<\/p>\n\n\n\n<p>\u00a0$3x + 20\u00a0 = 3 (10)\u00a0 + 20\u00a0 = 30 + 20 = 50$<\/p>\n\n\n\n<p>Thus, the value of each labeled angle is $50^{\\circ}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-alternate-angles\">Practice Problems on Alternate Angles<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Alternate Angles: Definition, Types, Theorem, Examples, Facts<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">From the image given below, identify the pair of alternate interior angles.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-angles-example-1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">1 and 2<\/div><div class=\"spq_answer_block\" data-value=\"1\">2 and 4<\/div><div class=\"spq_answer_block\" data-value=\"2\">2 and 6<\/div><div class=\"spq_answer_block\" data-value=\"3\">3 and 6<\/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: 3 and 6<br\/>The pair of angles on the inner side of the two parallel lines but on the other side of the transversal are known as alternate interior angles. Thus, 3 and 6 are alternate interior angles.<\/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\">In the given diagram, angles X and Y are<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">alternate angles<\/div><div class=\"spq_answer_block\" data-value=\"1\">corresponding angles<\/div><div class=\"spq_answer_block\" data-value=\"2\">exterior angles<\/div><div class=\"spq_answer_block\" data-value=\"3\">co-interior angles.<\/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: corresponding angles<br\/>Angles X and Y are corresponding angles. They are formed at matching\/corresponding corners with respect to the transversal.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Name the angle relationship in the diagram given below:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Alternate Interior Angles<\/div><div class=\"spq_answer_block\" data-value=\"1\">Alternate exterior Angles<\/div><div class=\"spq_answer_block\" data-value=\"2\">Corresponding Angles<\/div><div class=\"spq_answer_block\" data-value=\"3\">Vertical Angles<\/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: Alternate exterior Angles<br\/>The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles. Thus, the angles 1 and 2 are alternate exterior angles.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Angles inside a pair of parallel lines that lie on the opposite sides of a transversal and are congruent are called _____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Vertical angles<\/div><div class=\"spq_answer_block\" data-value=\"1\">Corresponding Angles<\/div><div class=\"spq_answer_block\" data-value=\"2\">Supplementary Angles<\/div><div class=\"spq_answer_block\" data-value=\"3\">Alternate Interior Angles<\/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: Alternate Interior Angles<br\/>The pair of angles on the inner side of the two lines but on the other side of the transversal are known as alternate interior angles.<\/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\": \"Alternate Angles: Definition, Types, Theorem, Examples, Facts\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Alternate Angles\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"From the image given below, identify the pair of alternate interior angles.\",\n                    \"text\": \"From the image given below, identify the pair of alternate interior angles. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/alternate-angles-example-1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The pair of angles on the inner side of the two parallel lines but on the other side of the transversal are known as alternate interior angles. Thus, 3 and 6 are alternate interior angles.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1 and 2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The pair of angles on the inner side of the two parallel lines but on the other side of the transversal are known as alternate interior angles. Thus, 3 and 6 are alternate interior angles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2 and 4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The pair of angles on the inner side of the two parallel lines but on the other side of the transversal are known as alternate interior angles. Thus, 3 and 6 are alternate interior angles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2 and 6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The pair of angles on the inner side of the two parallel lines but on the other side of the transversal are known as alternate interior angles. Thus, 3 and 6 are alternate interior angles.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"3 and 6\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The pair of angles on the inner side of the two parallel lines but on the other side of the transversal are known as alternate interior angles. Thus, 3 and 6 are alternate interior angles.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The pair of angles on the inner side of the two parallel lines but on the other side of the transversal are known as alternate interior angles. Thus, 3 and 6 are alternate interior angles.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In the given diagram, angles X and Y are\",\n                    \"text\": \"In the given diagram, angles X and Y are\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Angles X and Y are corresponding angles. They are formed at matching\/corresponding corners with respect to the transversal.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"alternate angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Angles X and Y are corresponding angles. They are formed at matching\/corresponding corners with respect to the transversal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"exterior angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Angles X and Y are corresponding angles. They are formed at matching\/corresponding corners with respect to the transversal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"co-interior angles.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Angles X and Y are corresponding angles. They are formed at matching\/corresponding corners with respect to the transversal.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"corresponding angles\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Angles X and Y are corresponding angles. They are formed at matching\/corresponding corners with respect to the transversal.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Angles X and Y are corresponding angles. They are formed at matching\/corresponding corners with respect to the transversal.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Name the angle relationship in the diagram given below:\",\n                    \"text\": \"Name the angle relationship in the diagram given below:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles. Thus, the angles 1 and 2 are alternate exterior angles.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Alternate Interior Angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles. Thus, the angles 1 and 2 are alternate exterior angles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Corresponding Angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles. Thus, the angles 1 and 2 are alternate exterior angles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Vertical Angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles. Thus, the angles 1 and 2 are alternate exterior angles.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Alternate exterior Angles\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles. Thus, the angles 1 and 2 are alternate exterior angles.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles. Thus, the angles 1 and 2 are alternate exterior angles.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Angles inside a pair of parallel lines that lie on the opposite sides of a transversal and are congruent are called _____.\",\n                    \"text\": \"Angles inside a pair of parallel lines that lie on the opposite sides of a transversal and are congruent are called _____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The pair of angles on the inner side of the two lines but on the other side of the transversal are known as alternate interior angles.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Vertical angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The pair of angles on the inner side of the two lines but on the other side of the transversal are known as alternate interior angles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Corresponding Angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The pair of angles on the inner side of the two lines but on the other side of the transversal are known as alternate interior angles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Supplementary Angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The pair of angles on the inner side of the two lines but on the other side of the transversal are known as alternate interior angles.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Alternate Interior Angles\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The pair of angles on the inner side of the two lines but on the other side of the transversal are known as alternate interior angles.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The pair of angles on the inner side of the two lines but on the other side of the transversal are known as alternate interior angles.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-about-alternate-angles\">Frequently Asked Questions about Alternate Angles<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\" 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-0-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\"><strong>What are the corresponding 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-0-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\">\n\n<p>When two lines are crossed by a transversal, the angles formed in the matching corners are called corresponding angles.When the two lines are parallel, corresponding angles are equal.<\/p>\n\n\n\n<p>Take a look at the image given below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"231\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/angles-formed-by-parallel-lines-and-transversal.png\" alt=\"Corresponding angles\" class=\"wp-image-31725\" title=\"Corresponding angles\"\/><\/figure>\n\n\n\n<p>In the above image,&nbsp;<\/p>\n\n\n\n<p>angle 3 corresponds to angle 7,&nbsp;<\/p>\n\n\n\n<p>angle 4 corresponds to angle 8,&nbsp;<\/p>\n\n\n\n<p>angle 1 corresponds to angle 5,&nbsp;<\/p>\n\n\n\n<p>angle 2 corresponds to angle 6.<\/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-1-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\"><strong>What is the difference between alternate angles and corresponding 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-1-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\">\n\n<p>Alternate angles are defined as angles in a plane figure that lie on opposite sides of a transversal line and have the same measurements. In the image given below, 1 and 7, 4 and 6, 2 and 8, 3 and 5 are alternate angles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"291\" height=\"230\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/different-angles.png\" alt=\"Corresponding and alternate angles\" class=\"wp-image-31727\" title=\"Corresponding and alternate angles\"\/><\/figure>\n\n\n\n<p>On the other hand, corresponding angles are angles that are in the same relative positions along the transversal line and still have the same measurements.<\/p>\n\n\n\n<p>In the image given above, 1 and 5, 4 and 8, 2 and 6, 3 and 7 are pairs of corresponding 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-2-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\"><strong>What are the same side 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-2-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\">\n\n<p>The same side interior angles formed by a transversal cutting two parallel lines are shown in the figure below. They are supplementary.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"291\" height=\"257\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/identifying-alternate-interior-angles.png\" alt=\"Same side interior angles\" class=\"wp-image-31728\" title=\"Same side interior angles\"\/><\/figure>\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-3-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\"><strong>How do you prove that the sum of the three interior angles of a triangle is 180 degrees?<\/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-3-54ea40e0-79b3-4fbd-bb9d-326f14ed2239\">\n\n<p>If we have a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangle<\/a>, we can always draw two parallel lines as shown in the figure.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"274\" height=\"151\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/triangle-sum-property.png\" alt=\"Angle sum property of a triangle\" class=\"wp-image-31729\" title=\"Angle sum property of a triangle\"\/><\/figure>\n\n\n\n<p>Now, AB and AC are the transversals. We know that alternate angles are equal. Therefore, the two angles labeled as x are equal. Also, the two angles labeled y are equal.<\/p>\n\n\n\n<p>We know that x, y, and z together add up to 180 degrees, because together, these are just angles in a linear pair or the angles around the straight line.\u00a0So, $x + y + z = 180^{\\circ}$<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Alternate Angles? When a transversal cuts a pair of parallel lines (or non-parallel lines), it forms different types of angles. Alternate interior angles are a set of non-adjacent angles on either side of the transversal. In each diagram given below, two parallel lines are cut by a transversal. All the angle pairs highlighted &#8230; <a title=\"Alternate Angles: Definition, Types, Theorem, Examples, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-angles\" aria-label=\"More on Alternate Angles: Definition, Types, Theorem, 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-31709","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\/31709","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=31709"}],"version-history":[{"count":13,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31709\/revisions"}],"predecessor-version":[{"id":31749,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31709\/revisions\/31749"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=31709"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=31709"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=31709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}