{"id":35119,"date":"2023-10-20T18:52:00","date_gmt":"2023-10-20T18:52:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=35119"},"modified":"2023-10-22T07:14:55","modified_gmt":"2023-10-22T07:14:55","slug":"alternate-exterior-angles-definition-theorem-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-exterior-angles","title":{"rendered":"Alternate Exterior Angles &#8211; Definition, Theorem, Examples, FAQs"},"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-f029f732-35df-4aa1-a217-e213abd2fe68\" 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-exterior-angles#0-what-are-alternate-exterior-angles>What Are Alternate Exterior Angles?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-exterior-angles#3-proof-of-alternate-exterior-angles-theorem>Proof of Alternate Exterior Angles Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-exterior-angles#4-converse-of-alternate-exterior-angles-theorem>Converse of Alternate Exterior Angles Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-exterior-angles#7-solved%C2%A0-examples-on-alternate-exterior-angles>Solved\u00a0 Examples on Alternate Exterior Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-exterior-angles#8-practice-problems-on-alternate-exterior-angles>Practice Problems on Alternate Exterior Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-exterior-angles#9-frequently-asked-questions-about-alternate-exterior-angles>Frequently Asked Questions about Alternate Exterior Angles<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-alternate-exterior-angles\">What Are Alternate Exterior Angles?<\/h2>\n\n\n\n<p><strong>When two lines (<\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/parallel-lines\"><strong>parallel lines<\/strong><\/a><strong>) are cut by a transversal at two distinct lines, a pair of <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/angle\"><strong>angles <\/strong><\/a><strong>that are created on the alternate sides of a transversal and on the outer side (exterior side) of the two lines are called alternate exterior angles.<\/strong><\/p>\n\n\n\n<p><strong>What do alternate exterior angles look like?<\/strong><\/p>\n\n\n\n<p>The diagram on the left side shows the alternate exterior angles formed by two non-parallel lines cut by transversal. The diagram on the right shows the alternate exterior angles formed by two parallel lines cut by transversal.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"429\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-exterior-angles.png\" alt=\"Alternate exterior angles\" class=\"wp-image-35125\" title=\"Alternate exterior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-exterior-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-exterior-angles-300x208.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-alternate-exterior-angles-definition\">Alternate Exterior Angles: Definition<\/h2>\n\n\n\n<p><strong>Definition of alternate exterior angles: <\/strong>A pair of angles formed on the alternate sides (opposite sides) of a transversal and on the exterior side of two <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/line\">lines<\/a> cut by transversal are known as alternate exterior angles.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"335\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-exterior-angles-.png\" alt=\"Alternate exterior angles\" class=\"wp-image-35126\" title=\"Alternate exterior angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-exterior-angles-.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/alternate-exterior-angles--300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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-alternate-exterior-angles-theorem\">Alternate Exterior Angles Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-8bc48a12-cd9d-43c9-8f5c-fe54f017876e\">\n\n\n<p>The alternate exterior angle theorem states that when two parallel lines are cut by a transversal, then the pair of alternate exterior angles formed are congruent.<\/p>\n\n\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"3-proof-of-alternate-exterior-angles-theorem\">Proof of Alternate Exterior Angles Theorem<\/h2>\n\n\n\n<p><strong>Given<\/strong>: l || m and t is a transversal.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/akWaJH64rbwgXIGIIloN1m1h-lqXovqiiov9cALYlHOwFBGrgbyVRQqeWTR6O5fTWdEOgakwrTjRlzh6A1tChFKvsCz_MLwlpHQwl1n2iMSGwW6tMKsAxvyfHMGMVDEAyMRBtm0iygy3oDtxf-I8Cbs\" alt=\"\"\/><\/figure>\n\n\n\n<p>Alt tag: Parallel lines l and m cut by a transversal<\/p>\n\n\n\n<p><strong>To prove:<\/strong>&nbsp;<\/p>\n\n\n\n<p>m\u22201 = m\u22208<\/p>\n\n\n\n<p>m\u22202 = m\u22207<\/p>\n\n\n\n<p><strong>Proof:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th><strong>Statement<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Reasoning<\/strong><\/th><\/tr><\/thead><tbody><tr><td>m\u22201 = m\u22204<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/vertical-angles#:~:text=Vertically%20opposite%20angles%20are%20always,%C2%B0%20%2B%20%E2%88%A0BCE%20%3D%20180%C2%B0\">Vertically opposite angles<\/a><\/td><\/tr><tr><td>m\u22204 = m\u22208<\/td><td class=\"has-text-align-left\" data-align=\"left\">Corresponding angles formed by two parallel lines cut by a transversal are congruent.<\/td><\/tr><tr><td>m\u22201 = m\u22208<\/td><td class=\"has-text-align-left\" data-align=\"left\">by Transitive property<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Hence, proved.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-converse-of-alternate-exterior-angles-theorem\">Converse of Alternate Exterior Angles Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-921164d4-bd38-403c-8bff-04742a27b468\">\n\n\n<p>The converse of alternate exterior angles theorem states that if the alternate exterior angles formed by two lines cut by a transversal are congruent, then the two lines are parallel to one another.<\/p>\n\n\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"5-facts-about-alternate-exterior-angles\">Facts about Alternate Exterior 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 exterior angles theorem is used to prove that two lines are parallel to each other.<\/li>\n\n\n\n<li>If the lines are not parallel, the alternate exterior angles are not congruent and do not have any relationship.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about<strong> <\/strong>Alternate Exterior Angles. We discussed the definition, the alternate exterior angles theorem, converse, and the proof. Let\u2019s solve a few examples and practice problems for better comprehension.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-solved%C2%A0-examples-on-alternate-exterior-angles\">Solved\u00a0 Examples on Alternate Exterior Angles<\/h2>\n\n\n\n<p><strong>Example 1: Find the value of x.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"299\" height=\"273\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/figure-representing-alternate-exterior-angles.png\" alt=\"Figure representing alternate exterior angles\" class=\"wp-image-35128\" title=\"Figure representing alternate exterior angles\"\/><\/figure>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>m\u2220EFH = 130<sup>o<\/sup><\/p>\n\n\n\n<p>m\u2220ACB = x<\/p>\n\n\n\n<p>Here, m\u2220EFH + m\u2220GFH = 180<sup>o<\/sup> \u2026angles in a linear pair<\/p>\n\n\n\n<p>Thus, 130 + m\u2220GFH = 180<sup>o<\/sup><\/p>\n\n\n\n<p>m\u2220GFH = 180<sup>o<\/sup> &#8211; 130<sup>o<\/sup><\/p>\n\n\n\n<p>m\u2220GFH = 50<sup>o<\/sup><\/p>\n\n\n\n<p>Now, m\u2220GFH = x \u2026Alternate Exterior Angles Theorem<\/p>\n\n\n\n<p>Thus, x = 50<sup>o<\/sup><\/p>\n\n\n\n<p><strong>Example 2: If two alternate exterior angles formed by two lines and a transversal are <\/strong><strong>(2x + 10) <\/strong><strong>and <\/strong><strong>(4x &#8211; 20)<\/strong><strong>, then what should the value of x be such that two lines are parallel?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>For two lines to be parallel, the alternate exterior angles should be equal to each other.&nbsp;<\/p>\n\n\n\n<p>2x + 10 = 4x &#8211; 20<\/p>\n\n\n\n<p>4x &#8211; 2x = 20 + 10<\/p>\n\n\n\n<p>2x = 30<\/p>\n\n\n\n<p>$x = \\frac{30}{2}$<\/p>\n\n\n\n<p>x = 15<\/p>\n\n\n\n<p>Thus, the two lines will be parallel for x = 15.<\/p>\n\n\n\n<p><strong>Example 3: Find the value of y if the two parallel lines are cut by a transversal.&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"297\" height=\"218\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/figure-showing-alternate-exterior-angles-in-variable-form.png\" alt=\"Figure showing alternate exterior angles in variable form\" class=\"wp-image-35129\" title=\"Figure showing alternate exterior angles in variable form\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>The given angles (3y + 49) and (7y &#8211; 55) are alternate exterior angles.<\/p>\n\n\n\n<p>By the alternate exterior angles theorem, we have<\/p>\n\n\n\n<p>(3y + 49) = (7y &#8211; 55)&nbsp;<\/p>\n\n\n\n<p>4y = 104<\/p>\n\n\n\n<p>y=26<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-practice-problems-on-alternate-exterior-angles\">Practice Problems on Alternate Exterior Angles<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Alternate Exterior Angles - Definition, Theorem, Examples, FAQs<\/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\">Alternate exterior angles formed by two parallel lines cut by a transversal are<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Congruent<\/div><div class=\"spq_answer_block\" data-value=\"1\">Non-congruent<\/div><div class=\"spq_answer_block\" data-value=\"2\">complementary<\/div><div class=\"spq_answer_block\" data-value=\"3\">supplementary<\/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: Congruent<br\/>Alternate exterior angles are congruent when the two lines cut by a transversal are parallel.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Find m\u22202.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/Parallel-lines-m-and-n-cut-by-a-transversal-l-forming-alternate-exterior-angles.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$120^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$30^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$60^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$15^{\\circ}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $60^{\\circ}$<br\/>Alternate exterior angles formed by two parallel lines cut by a transversal are congruent.<br>\r\nThe $60^{\\circ}$ angle and \u22202 are alternate exterior angles formed by two parallel lines m and n cut by a transversal l are congruent.<br>\r\nThus, m\u22202 $= 60^{\\circ}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Alternate exterior angles lie on the ______of  the transversal.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">opposite sides<\/div><div class=\"spq_answer_block\" data-value=\"1\">Same side<\/div><div class=\"spq_answer_block\" data-value=\"2\">outer sides<\/div><div class=\"spq_answer_block\" data-value=\"3\">inner side<\/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\/>Alternate exterior angles lie on the opposite sides of the transversal.<\/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\">Alternate exterior angles lie on the _____ of the parallel sides.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">opposite side<\/div><div class=\"spq_answer_block\" data-value=\"1\">same side<\/div><div class=\"spq_answer_block\" data-value=\"2\">interior region<\/div><div class=\"spq_answer_block\" data-value=\"3\">outer side<\/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: outer side<br\/>Alternate exterior angles lie on the outer side of the parallel sides.<\/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 Exterior Angles - Definition, Theorem, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Alternate Exterior Angles\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Alternate exterior angles formed by two parallel lines cut by a transversal are\",\n                    \"text\": \"Alternate exterior angles formed by two parallel lines cut by a transversal are\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Alternate exterior angles are congruent when the two lines cut by a transversal are parallel.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Non-congruent\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles are congruent when the two lines cut by a transversal are parallel.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"complementary\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles are congruent when the two lines cut by a transversal are parallel.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"supplementary\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles are congruent when the two lines cut by a transversal are parallel.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Congruent\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Alternate exterior angles are congruent when the two lines cut by a transversal are parallel.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Alternate exterior angles are congruent when the two lines cut by a transversal are parallel.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find m\u22202.\",\n                    \"text\": \"Find m\u22202. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/Parallel-lines-m-and-n-cut-by-a-transversal-l-forming-alternate-exterior-angles.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Alternate exterior angles formed by two parallel lines cut by a transversal are congruent.<br>\r\nThe $$60^{\\\\circ}$$ angle and \u22202 are alternate exterior angles formed by two parallel lines m and n cut by a transversal l are congruent.<br>\r\nThus, m\u22202 $$= 60^{\\\\circ}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$120^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles formed by two parallel lines cut by a transversal are congruent.<br>\r\nThe $$60^{\\\\circ}$$ angle and \u22202 are alternate exterior angles formed by two parallel lines m and n cut by a transversal l are congruent.<br>\r\nThus, m\u22202 $$= 60^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$30^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles formed by two parallel lines cut by a transversal are congruent.<br>\r\nThe $$60^{\\\\circ}$$ angle and \u22202 are alternate exterior angles formed by two parallel lines m and n cut by a transversal l are congruent.<br>\r\nThus, m\u22202 $$= 60^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$15^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles formed by two parallel lines cut by a transversal are congruent.<br>\r\nThe $$60^{\\\\circ}$$ angle and \u22202 are alternate exterior angles formed by two parallel lines m and n cut by a transversal l are congruent.<br>\r\nThus, m\u22202 $$= 60^{\\\\circ}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$60^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Alternate exterior angles formed by two parallel lines cut by a transversal are congruent.<br>\r\nThe $$60^{\\\\circ}$$ angle and \u22202 are alternate exterior angles formed by two parallel lines m and n cut by a transversal l are congruent.<br>\r\nThus, m\u22202 $$= 60^{\\\\circ}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Alternate exterior angles formed by two parallel lines cut by a transversal are congruent.<br>\r\nThe $$60^{\\\\circ}$$ angle and \u22202 are alternate exterior angles formed by two parallel lines m and n cut by a transversal l are congruent.<br>\r\nThus, m\u22202 $$= 60^{\\\\circ}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Alternate exterior angles lie on the ______of  the transversal.\",\n                    \"text\": \"Alternate exterior angles lie on the ______of  the transversal.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Alternate exterior angles lie on the opposite sides of the transversal.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Same side\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles lie on the opposite sides of the transversal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"outer sides\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles lie on the opposite sides of the transversal.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"inner side\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles lie on the opposite sides of the transversal.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"opposite sides\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Alternate exterior angles lie on the opposite sides of the transversal.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Alternate exterior angles lie on the opposite sides of the transversal.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Alternate exterior angles lie on the _____ of the parallel sides.\",\n                    \"text\": \"Alternate exterior angles lie on the _____ of the parallel sides.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Alternate exterior angles lie on the outer side of the parallel sides.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"opposite side\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles lie on the outer side of the parallel sides.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"same side\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles lie on the outer side of the parallel sides.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"interior region\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Alternate exterior angles lie on the outer side of the parallel sides.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"outer side\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Alternate exterior angles lie on the outer side of the parallel sides.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Alternate exterior angles lie on the outer side of the parallel sides.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-frequently-asked-questions-about-alternate-exterior-angles\">Frequently Asked Questions about Alternate Exterior Angles<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-78025c3a-99ea-46c2-abcd-98fa31c60b77\" 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-0-78025c3a-99ea-46c2-abcd-98fa31c60b77\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-78025c3a-99ea-46c2-abcd-98fa31c60b77\"><strong>What are 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-0-78025c3a-99ea-46c2-abcd-98fa31c60b77\">\n\n<p>Alternate interior angles are a pair of angles that are on opposite sides of a transversal line and inside the two intersected lines.<\/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-1-78025c3a-99ea-46c2-abcd-98fa31c60b77\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-78025c3a-99ea-46c2-abcd-98fa31c60b77\"><strong>Is the alternate exterior angles theorem applicable when more than two parallel lines cut by a transversal?<\/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-1-78025c3a-99ea-46c2-abcd-98fa31c60b77\">\n\n<p>Yes, we can extend the alternate exterior angles theorem to more than two parallel lines cut by a transversal.<\/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-2-78025c3a-99ea-46c2-abcd-98fa31c60b77\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-78025c3a-99ea-46c2-abcd-98fa31c60b77\"><strong>Are alternate 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-2-78025c3a-99ea-46c2-abcd-98fa31c60b77\">\n\n<p>Alternate angles are not supplementary angles, but they will add up to 180 if the transversal is perpendicular to the parallel lines.<\/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-3-78025c3a-99ea-46c2-abcd-98fa31c60b77\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-78025c3a-99ea-46c2-abcd-98fa31c60b77\"><strong>Are alternate exterior angles congruent?<\/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-3-78025c3a-99ea-46c2-abcd-98fa31c60b77\">\n\n<p>Alternate exterior angles formed when two parallel lines are cut by a transversal are congruent.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Alternate Exterior Angles? When two lines (parallel lines) are cut by a transversal at two distinct lines, a pair of angles that are created on the alternate sides of a transversal and on the outer side (exterior side) of the two lines are called alternate exterior angles. What do alternate exterior angles look &#8230; <a title=\"Alternate Exterior Angles &#8211; Definition, Theorem, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/alternate-exterior-angles\" aria-label=\"More on Alternate Exterior Angles &#8211; Definition, Theorem, Examples, FAQs\">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-35119","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\/35119","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=35119"}],"version-history":[{"count":8,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35119\/revisions"}],"predecessor-version":[{"id":35136,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35119\/revisions\/35136"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=35119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=35119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=35119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}