{"id":34720,"date":"2023-10-06T05:39:55","date_gmt":"2023-10-06T05:39:55","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=34720"},"modified":"2023-12-13T11:48:56","modified_gmt":"2023-12-13T11:48:56","slug":"alternate-interior-angles-definition-theorems-examples-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-interior-angles","title":{"rendered":"Alternate Interior Angles &#8211; Definition, Theorems, 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-45d910e6-6d7c-49c8-86b9-5cef26fd2f57\" 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-interior-angles#0-what-are-alternate-interior-angles-in-geometry>What Are Alternate Interior Angles in Geometry?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-interior-angles#2-how-to-find-the-alternate-interior-angles>How to Find the Alternate Interior Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-interior-angles#5-converse-of-the-alternate-interior-angles-theorem>Converse of the Alternate Interior Angles Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-interior-angles#8-solved-examples-on-alternate-interior-angles>Solved Examples on Alternate Interior Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-interior-angles#9-practice-problems-on-alternate-interior-angles>Practice Problems on Alternate Interior Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-interior-angles#10-frequently-asked-questions-about-alternate-interior-angles>Frequently Asked Questions about Alternate Interior Angles<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-alternate-interior-angles-in-geometry\">What Are Alternate Interior Angles in Geometry?<\/h2>\n\n\n\n<p><strong>When a transversal crosses two parallel lines (or non-parallel lines), the pair of nonadjacent angles formed on the inner side of the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-lines\"><strong>parallel lines<\/strong><\/a><strong>, but on the opposite sides of the transversal are known as alternate interior angles.&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"615\" height=\"406\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles.png\" alt=\"Alternate interior angles\" class=\"wp-image-34726\" title=\"Alternate interior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles.png 615w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-300x198.png 300w\" sizes=\"auto, (max-width: 615px) 100vw, 615px\" \/><\/figure>\n\n\n\n<p>The following diagram shows alternate interior angles formed in two cases:&nbsp;<\/p>\n\n\n\n<p>i) parallel lines cut by a transversal<\/p>\n\n\n\n<p>ii) non-parallel lines cut by a transversal.<\/p>\n\n\n\n<p>Alternate interior angles are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u22202 and \u22203<\/li>\n\n\n\n<li>\u22201 and \u22204<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"406\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-formed-by-non-parallel-lines-and-parallel-lines.png\" alt=\"Alternate interior angles formed by non-parallel lines and parallel lines\" class=\"wp-image-34727\" title=\"Alternate interior angles formed by non-parallel lines and parallel lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-formed-by-non-parallel-lines-and-parallel-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-formed-by-non-parallel-lines-and-parallel-lines-300x196.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>If the lines are parallel, the alternate interior angles are always equal. In other words, the alternate interior angles can be used to prove whether the lines given are parallel or not. If the alternate interior angles are equal, then the given lines that are crossed by a transversal are said to be parallel.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-the-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_add_angles_pt.png\" alt=\"Add the Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add the Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-in-multiples-of-10-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_1_pt.png\" alt=\"Draw Angles in Multiples of 10 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles in Multiples of 10 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-nearest-5-and-1-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_2_pt.png\" alt=\"Draw Angles Nearest 5 and 1 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles Nearest 5 and 1 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-using-a-protractor\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_protractor_pt.png\" alt=\"Draw Angles Using a Protractor Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles Using a Protractor Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-right-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_right_angle_1_pt.png\" alt=\"Find Right Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Right Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-perimeter-of-the-squared-and-the-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_rectangle_2_pt.png\" alt=\"Find the Perimeter of the Squared and the Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Perimeter of the Squared and the Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-angles-by-their-types\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_types_of_angle_pt.png\" alt=\"Identify Angles by their Types Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Angles by their Types Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        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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-alternate-interior-angles-definition\">Alternate Interior Angles: Definition<\/h2>\n\n\n\n<p>A pair of nonadjacent angles formed on the alternate side of the transversal but lying in between the two lines cut by the transversal are called alternate interior angles.<\/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        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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-how-to-find-the-alternate-interior-angles\">How to Find the Alternate Interior Angles<\/h2>\n\n\n\n<p>It is very easy to locate or identify the alternate interior angles due to their position. They together make a Z-shape or Z-pattern. They lie in the interior region between two lines, but on the opposite side of the transversal.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"470\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-making-Z-pattern.png\" alt=\"Alternate interior angles making Z-pattern\" class=\"wp-image-34729\" title=\"Alternate interior angles making Z-pattern\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-making-Z-pattern.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-making-Z-pattern-300x227.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-properties-of-alternate-interior-angles\">Properties of Alternate Interior Angles<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When two parallel lines cut by a transversal, the alternate Interior angles formed are congruent.<\/li>\n\n\n\n<li>They share one common arm. They do not share a common vertex.<\/li>\n\n\n\n<li>Alternate interior angles don\u2019t have any specific properties in case of non \u2013 parallel lines.<\/li>\n\n\n\n<li>If two non-parallel lines are cut by a transversal, the alternate Interior angles formed are not congruent.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-alternate-interior-angles-theorem-and-proof\">Alternate Interior Angles Theorem and Proof<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-2171a2a8-3985-45df-82a8-073350f9cf0c\">\n\n\n<p><strong>Statement:<\/strong> If a transversal crosses two or more parallel lines, the alternate interior angles are congruent.<\/p>\n\n\n<\/div>\n\n\n<p><strong>Given: <\/strong>a \u2225 d<\/p>\n\n\n\n<p><strong>To prove: <\/strong>\u22204 = \u22205 and \u22203 = \u22206<\/p>\n\n\n\n<p><strong>Proof: <\/strong>Suppose line x is parallel to line y, and t is the transversal.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"445\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-theorem-diagram.png\" alt=\"Alternate interior angles theorem diagram\" class=\"wp-image-34730\" title=\"Alternate interior angles theorem diagram\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-theorem-diagram.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-interior-angles-theorem-diagram-300x215.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>We know that if a transversal cuts any two parallel lines, the corresponding angles and vertically opposite angles are equal to each other. Therefore,<\/p>\n\n\n\n<p>m\u22202 = m\u22205 \u2026\u2026\u2026..(i) [Corresponding angles]<\/p>\n\n\n\n<p>m\u22202 = m\u22204 \u2026\u2026\u2026..(ii) [Vertically opposite angles]<\/p>\n\n\n\n<p>From (i) and (ii), we get<\/p>\n\n\n\n<p>m\u22204 = m\u22205<\/p>\n\n\n\n<p>Similarly,<\/p>\n\n\n\n<p>m\u22203 = m\u22206<\/p>\n\n\n\n<p>Hence, proved.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-converse-of-the-alternate-interior-angles-theorem\">Converse of the Alternate Interior Angles Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-1119caf9-4481-493a-a1c1-fb7d6d808995\">\n\n\n<p><strong>Statement: <\/strong>If a transversal intersects two lines such that the alternate interior angles are equal, then the two lines are parallel.<\/p>\n\n\n<\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"457\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converse-of-alternate-interior-angles-theorem.png\" alt=\"Converse of alternate interior angles theorem\" class=\"wp-image-34731\" title=\"Converse of alternate interior angles theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converse-of-alternate-interior-angles-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/converse-of-alternate-interior-angles-theorem-300x221.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>m\u22201 = m\u22203 (given)&nbsp;<\/p>\n\n\n\n<p>m\u22203 = m\u22205 (vertically opposite angles)<\/p>\n\n\n\n<p>Hence, m\u22201 = m\u22205. (by transitive property of equality)<\/p>\n\n\n\n<p>Similarly, we can prove that \u22202 = \u22204.&nbsp;<\/p>\n\n\n\n<p>However, the angle pairs \u22201-\u22205 and \u22202-\u22204 are pairs of corresponding angles.<\/p>\n\n\n\n<p>By the converse of the corresponding angles postulate, lines are parallel to each other.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-facts-about-alternate-interior-angles\">Facts about Alternate Interior Angles<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Alternate interior angles are a pair of non-adjacent angles that are located on opposite sides of the transversal and inside the two parallel lines.<\/li>\n\n\n\n<li>Alternate interior angles formed by parallel lines cut by a transversal are always congruent.<\/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 Alternate Interior Angles. We discussed important definitions and theorems associated with alternate interior angles. Let\u2019s solve a few examples and MCQs for hands-on practice!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-examples-on-alternate-interior-angles\">Solved Examples on Alternate Interior Angles<\/h2>\n\n\n\n<p><strong>1. Find the measure of <\/strong><strong>x<\/strong><strong> in the following figure.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"258\" height=\"282\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/finding-alternate-interior-angles.png\" alt=\"Finding alternate interior angles\" class=\"wp-image-34732\" title=\"Finding alternate interior angles\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>m \u2225 n and p is the transversal.<\/p>\n\n\n\n<p>The given angles are alternate interior angles.<\/p>\n\n\n\n<p>(5x)\u00b0 = (3x + 28)\u00b0<\/p>\n\n\n\n<p>(5x \u2013 3x)\u00b0 = 28\u00b0<\/p>\n\n\n\n<p>(2x)\u00b0 = 28\u00b0<\/p>\n\n\n\n<p>x = 14<\/p>\n\n\n\n<p><strong>2. Find the value of x and y in the following figure.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"304\" height=\"209\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/finding-unknown-angles-using-alternate-interior-angles-theorem.png\" alt=\"Finding unknown angles using alternate interior angles theorem\" class=\"wp-image-34733\" title=\"Finding unknown angles using alternate interior angles theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/finding-unknown-angles-using-alternate-interior-angles-theorem.png 304w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/finding-unknown-angles-using-alternate-interior-angles-theorem-300x206.png 300w\" sizes=\"auto, (max-width: 304px) 100vw, 304px\" \/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>x + 50\u00b0 = 180\u00b0 (Angles in a linear pair.)<\/p>\n\n\n\n<p>x = 180\u00b0 \u2013 50\u00b0&nbsp;<\/p>\n\n\n\n<p>x = 130\u00b0<\/p>\n\n\n\n<p>AB \u2225 CD and t is the transversal.<\/p>\n\n\n\n<p>y = x = 130\u00b0 (Alternate interior angles.)<\/p>\n\n\n\n<p><strong>3. What is the value of x in the following figure?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"272\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-based-on-alternate-interior-angles-theorem.png\" alt=\"Example based on alternate interior angles theorem\" class=\"wp-image-34734\" title=\"Example based on alternate interior angles theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-based-on-alternate-interior-angles-theorem.png 343w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/example-based-on-alternate-interior-angles-theorem-300x238.png 300w\" sizes=\"auto, (max-width: 343px) 100vw, 343px\" \/><\/figure>\n\n\n\n<p><strong>Solution<\/strong>:&nbsp;<\/p>\n\n\n\n<p>Two parallel lines are cut by a transversal. The given two angles are alternate interior angles. Thus, they are congruent.<\/p>\n\n\n\n<p>(3x \u2013 10) = 44<\/p>\n\n\n\n<p>3x = 44 + 10<\/p>\n\n\n\n<p>3x = 54<\/p>\n\n\n\n<p>x = 18<\/p>\n\n\n\n<p><strong>4. What is the measure of angles 1, 3, and 4?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"324\" height=\"231\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/finding-missing-angles-using-alternate-interior-angles.png\" alt=\"Finding missing angles using alternate interior angles\" class=\"wp-image-34735\" title=\"Finding missing angles using alternate interior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/finding-missing-angles-using-alternate-interior-angles.png 324w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/finding-missing-angles-using-alternate-interior-angles-300x214.png 300w\" sizes=\"auto, (max-width: 324px) 100vw, 324px\" \/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>m || n and l is the transversal.<\/p>\n\n\n\n<p>m\u22203 = 120\u00b0 (Alternate Interior Angles)<\/p>\n\n\n\n<p>m\u22203 + m\u22204 = 180\u00b0 (Angles in a linear pair)<\/p>\n\n\n\n<p>120\u00b0 + m\u22204 = 180\u00b0<\/p>\n\n\n\n<p>m\u22204 = 60\u00b0<\/p>\n\n\n\n<p>Similarly, m\u22201 + 120\u00b0 = 180\u00b0 (Angles in a linear pair)<\/p>\n\n\n\n<p>m\u22201 = 60\u00b0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-alternate-interior-angles\">Practice Problems on Alternate Interior Angles<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Alternate Interior Angles - Definition, Theorems, Examples, Facts<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The alternate interior angles formed when two parallel lines are cut by a transversal are<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">equal<\/div><div class=\"spq_answer_block\" data-value=\"1\">supplementary<\/div><div class=\"spq_answer_block\" data-value=\"2\">complementary<\/div><div class=\"spq_answer_block\" data-value=\"3\">acute<\/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: equal<br\/>According to the Alternate Interior Angles Theorem, the alternate interior angles are equal when two parallel lines are cut by a transversal.<\/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\">The alternate interior angles are formed on the _______ of the transversal.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">same sides<\/div><div class=\"spq_answer_block\" data-value=\"1\">opposite sides<\/div><div class=\"spq_answer_block\" data-value=\"2\">exterior region<\/div><div class=\"spq_answer_block\" data-value=\"3\">interior region<\/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: opposite sides<br\/>The alternate interior angles are formed on the opposite of the transversal and in the alternate positions in the interior region of the parallel lines.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The alternate interior angles form a _______ pattern.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">C-shaped<\/div><div class=\"spq_answer_block\" data-value=\"1\">U-shaped<\/div><div class=\"spq_answer_block\" data-value=\"2\">X-shaped<\/div><div class=\"spq_answer_block\" data-value=\"3\">Z-shaped<\/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: Z-shaped<br\/>Alternate interior angles form a Z-shaped pattern.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Find the value of z in the following figure.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/two-parallel-lines-cut-by-a-transversal.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">107\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">137\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">133\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">143\u00b0<\/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: 137\u00b0<br\/>x + 43\u00b0 = 180\u00b0 \t\t(Linear Pair)<br>\r\nx = 180\u00b0 \u2013 43\u00b0 = 137\u00b0<br>\r\nNow,<br>\r\nx = z \t\t\t\t(Alternate Interior angles)<br>\r\nz = 137\u00b0<\/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                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        \"text\": \"complementary\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the Alternate Interior Angles Theorem, the alternate interior angles are equal when two parallel lines are cut by a transversal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"acute\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the Alternate Interior Angles Theorem, the alternate interior angles are equal when two parallel lines are cut by a transversal.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"equal\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the Alternate Interior Angles Theorem, the alternate interior angles are equal when two parallel lines are cut by a transversal.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the Alternate Interior Angles Theorem, the alternate interior angles are equal when two parallel lines are cut by a transversal.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The alternate interior angles are formed on the _______ of the transversal.\",\n                    \"text\": \"The alternate interior angles are formed on the _______ of the transversal.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The alternate interior angles are formed on the opposite of the transversal and in the alternate positions in the interior region of the parallel lines.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"same sides\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The alternate interior angles are formed on the opposite of the transversal and in the alternate positions in the interior region of the parallel lines.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"exterior region\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The alternate interior angles are formed on the opposite of the transversal and in the alternate positions in the interior region of the parallel lines.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"interior region\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The alternate interior angles are formed on the opposite of the transversal and in the alternate positions in the interior region of the parallel lines.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"opposite sides\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The alternate interior angles are formed on the opposite of the transversal and in the alternate positions in the interior region of the parallel lines.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The alternate interior angles are formed on the opposite of the transversal and in the alternate positions in the interior region of the parallel lines.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The alternate interior angles form a _______ pattern.\",\n                    \"text\": \"The alternate interior angles form a _______ pattern.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Alternate interior angles form a Z-shaped pattern.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"C-shaped\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate interior angles form a Z-shaped pattern.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"U-shaped\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate interior angles form a Z-shaped pattern.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"X-shaped\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate interior angles form a Z-shaped pattern.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Z-shaped\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Alternate interior angles form a Z-shaped pattern.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Alternate interior angles form a Z-shaped pattern.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the value of z in the following figure.\",\n                    \"text\": \"Find the value of z in the following figure. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/two-parallel-lines-cut-by-a-transversal.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"x + 43\u00b0 = 180\u00b0 \t\t(Linear Pair)<br>\r\nx = 180\u00b0 \u2013 43\u00b0 = 137\u00b0<br>\r\nNow,<br>\r\nx = z \t\t\t\t(Alternate Interior angles)<br>\r\nz = 137\u00b0\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"107\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"x + 43\u00b0 = 180\u00b0 \t\t(Linear Pair)<br>\r\nx = 180\u00b0 \u2013 43\u00b0 = 137\u00b0<br>\r\nNow,<br>\r\nx = z \t\t\t\t(Alternate Interior angles)<br>\r\nz = 137\u00b0\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"133\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"x + 43\u00b0 = 180\u00b0 \t\t(Linear Pair)<br>\r\nx = 180\u00b0 \u2013 43\u00b0 = 137\u00b0<br>\r\nNow,<br>\r\nx = z \t\t\t\t(Alternate Interior angles)<br>\r\nz = 137\u00b0\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"143\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"x + 43\u00b0 = 180\u00b0 \t\t(Linear Pair)<br>\r\nx = 180\u00b0 \u2013 43\u00b0 = 137\u00b0<br>\r\nNow,<br>\r\nx = z \t\t\t\t(Alternate Interior angles)<br>\r\nz = 137\u00b0\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"137\u00b0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"x + 43\u00b0 = 180\u00b0 \t\t(Linear Pair)<br>\r\nx = 180\u00b0 \u2013 43\u00b0 = 137\u00b0<br>\r\nNow,<br>\r\nx = z \t\t\t\t(Alternate Interior angles)<br>\r\nz = 137\u00b0\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"x + 43\u00b0 = 180\u00b0 \t\t(Linear Pair)<br>\r\nx = 180\u00b0 \u2013 43\u00b0 = 137\u00b0<br>\r\nNow,<br>\r\nx = z \t\t\t\t(Alternate Interior angles)<br>\r\nz = 137\u00b0\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-about-alternate-interior-angles\">Frequently Asked Questions about Alternate Interior Angles<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-170d94ef-e3af-4068-a6d6-5995432cacb6\" 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-0-170d94ef-e3af-4068-a6d6-5995432cacb6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-170d94ef-e3af-4068-a6d6-5995432cacb6\"><strong>Are alternate iInterior angles supplementary?<\/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-0-170d94ef-e3af-4068-a6d6-5995432cacb6\">\n\n<p>The alternate interior angles formed when two parallel lines are crossed by a transversal are congruent, not supplementary.<\/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-1-170d94ef-e3af-4068-a6d6-5995432cacb6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-170d94ef-e3af-4068-a6d6-5995432cacb6\"><strong>What is the other name for Alternate 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-1-170d94ef-e3af-4068-a6d6-5995432cacb6\">\n\n<p>The other name for Alternate Interior Angles is \u2018Z\u2019 Angles as they form a Z.<\/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-2-170d94ef-e3af-4068-a6d6-5995432cacb6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-170d94ef-e3af-4068-a6d6-5995432cacb6\"><strong>Are alternate interior angles always equal?<\/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-2-170d94ef-e3af-4068-a6d6-5995432cacb6\">\n\n<p>No, alternate interior angles are not always equal. They are equal only when the lines are parallel.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-170d94ef-e3af-4068-a6d6-5995432cacb6\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-170d94ef-e3af-4068-a6d6-5995432cacb6\"><strong>What are co-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-3-170d94ef-e3af-4068-a6d6-5995432cacb6\">\n\n<p>Co-interior angles or same-side interior angles are the pair of angles formed on the same side of the transversal and in the interior region of the two parallel lines.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Alternate Interior Angles in Geometry? When a transversal crosses two parallel lines (or non-parallel lines), the pair of nonadjacent angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are known as alternate interior angles.&nbsp; The following diagram shows alternate interior angles formed in two &#8230; <a title=\"Alternate Interior Angles &#8211; Definition, Theorems, Examples, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-interior-angles\" aria-label=\"More on Alternate Interior Angles &#8211; Definition, Theorems, 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-34720","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\/34720","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=34720"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34720\/revisions"}],"predecessor-version":[{"id":36533,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34720\/revisions\/36533"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=34720"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=34720"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=34720"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}