{"id":28113,"date":"2023-04-27T13:25:03","date_gmt":"2023-04-27T13:25:03","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=28113"},"modified":"2024-01-23T06:27:02","modified_gmt":"2024-01-23T06:27:02","slug":"exterior-angle-theorem-definition-proof-examples-facts-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/exterior-angle-theorem","title":{"rendered":"Exterior Angle Theorem: Definition, Proof, Examples, Facts, 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-ccf9d45c-5c7c-45c4-a770-81739e823bc9\" 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\/exterior-angle-theorem#0-what-is-the-exterior-angle-theorem>What Is the Exterior Angle Theorem?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exterior-angle-theorem#1-exterior-angle-theorem-statement>Exterior Angle Theorem Statement<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exterior-angle-theorem#2-proof-of-exterior-angle-theorem>Proof of Exterior Angle Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exterior-angle-theorem#7-solved-examples-on-exterior-angle-theorem>Solved Examples on Exterior Angle Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exterior-angle-theorem#8-practice-problems-on-exterior-angle-theorem>Practice Problems on Exterior Angle Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/exterior-angle-theorem#9-frequently-asked-questions-on-exterior-angle-theorem>Frequently Asked Questions on Exterior Angle Theorem<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-exterior-angle-theorem\">What Is the Exterior Angle Theorem?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The remote interior angles or opposite interior angles are the angles that are non-adjacent with the exterior angle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangle is a polygon with three sides. When we extend any side of a triangle, an angle is formed by the adjacent side and the extended ray. This angle is known as the \u201cexterior angle\u201d of a triangle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the figure given below, the exterior angle $\\angle ACD$ is formed by extending the side BC.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"326\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-of-a-triangle.png\" alt=\"Exterior angle of a triangle\" class=\"wp-image-37482\" title=\"Exterior angle of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-of-a-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-of-a-triangle-300x158.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 eplus-wrapper\" id=\"1-exterior-angle-theorem-statement\">Exterior Angle Theorem Statement<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>According to the exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite (remote) interior angles.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"341\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-theorem-visual-explanation.png\" alt=\"Exterior angle theorem visual explanation\" class=\"wp-image-37483\" title=\"Exterior angle theorem visual explanation\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-theorem-visual-explanation.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-theorem-visual-explanation-300x165.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Take a look at the triangle shown in the figure given below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"297\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-theorem-statement.png\" alt=\"Exterior Angle Theorem Statement\" class=\"wp-image-37484\" title=\"Exterior Angle Theorem Statement\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-theorem-statement.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-theorem-statement-300x144.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle BCD$ is the exterior angle and its two opposite interior angles are $\\angle A$ and $\\angle B$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the <strong>exterior angle theorem<\/strong>,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle BCD = \\angle A + \\angle B$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can use this theorem to find the measure of an unknown angle in a triangle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example: <\/strong>Find x.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-triangle-with-an-exterior-angle-x-and-remote-interior-angles-55-degree-and-45-degree.png\" alt=\"A triangle with an exterior angle x and remote interior angles 55\u00b0 and 45\u00b0\" class=\"wp-image-37485\" title=\"A triangle with an exterior angle x and remote interior angles 55\u00b0 and 45\u00b0\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-triangle-with-an-exterior-angle-x-and-remote-interior-angles-55-degree-and-45-degree.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/a-triangle-with-an-exterior-angle-x-and-remote-interior-angles-55-degree-and-45-degree-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, x is the exterior angle with two opposite interior angles measuring $55^\\circ$ and $45^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By the exterior angle theorem,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = 55^\\circ + 45^\\circ = 100^\\circ$<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/count-sides-and-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/count-sides-and-angles.jpeg\" alt=\"Count Sides and Angles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rectangles-and-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/separate-out-the-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/separate-out-the-triangles.jpeg\" alt=\"Separate Out the Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-proof-of-exterior-angle-theorem\">Proof of Exterior Angle Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can prove the exterior angle theorem using two methods.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-using-properties-of-triangles\">Using Properties of Triangles<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can prove the exterior angle theorem with the known properties of a triangle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider a $\\Delta ABC$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle ACD$ is the exterior angle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"327\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/triangle-abc-with-exterior-angle-acd.png\" alt=\"Triangle ABC with exterior angle ACD\" class=\"wp-image-37486\" title=\"Triangle ABC with exterior angle ACD\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/triangle-abc-with-exterior-angle-acd.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/triangle-abc-with-exterior-angle-acd-300x158.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle A + \\angle B + \\angle C = 180^\\circ$ (Angle Sum Property of a triangle) \u2026(1)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle C = 180^\\circ \\;\u2013\\; (\\angle A + \\angle B)$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2026(2)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle ACD = 180^\\circ \\;\u2013\\; \\angle C$ (Linear Pair of Angles) &nbsp; &nbsp; &nbsp; &nbsp; \u2026(3)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting the value of c in equation 3, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle ACD = 180^\\circ \\;-\\; \\left[180^\\circ \\;-\\; (\\angle A + \\angle B)\\right]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle ACD = 180^\\circ \\;-\\; 180^\\circ + (\\angle A + \\angle B)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle ACD = \\angle A + \\angle B$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence proved.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-using-properties-of-transversal-and-parallel-lines\">Using Properties of Transversal and Parallel Lines<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Given:<\/strong> Consider a $\\Delta ABC$ where a,b and c are the three interior angles.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Construction: <\/strong>Extend the side BC. Let D be any point on the extended side BC. Now an exterior angle, $\\angle ACD$&nbsp; is formed. Draw a line CE parallel to AB.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Angles 1 and 2 are the angles formed by the line CE such that<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$\\angle ACD= \\angle 1 + \\angle 2$&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"459\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/construction-for-the-proof-of-exterior-angle-theorem.png\" alt=\"Construction for the proof of exterior angle theorem\" class=\"wp-image-37487\" title=\"Construction for the proof of exterior angle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/construction-for-the-proof-of-exterior-angle-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/construction-for-the-proof-of-exterior-angle-theorem-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Proof:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$AB || CE$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">AC is the transversal.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, $\\angle a = \\angle 1$ (Pair of alternate angles)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$AB || CE$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">BD is the transversal.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, $\\angle b = \\angle 2$ (Pair of corresponding angles)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle ACD = \\angle 1 + \\angle 2$ (Construction)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting the value of $\\angle 1$ and $\\angle 2$, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle ACD = \\angle a + \\angle b$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, we proved that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-exterior-angle-inequality-theorem\">Exterior Angle Inequality Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than each of the opposite interior angles.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This theorem holds true for all the six exterior angles of a triangle.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"338\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-inequality-theorem.png\" alt=\"Exterior angle inequality theorem\" class=\"wp-image-37488\" title=\"Exterior angle inequality theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-inequality-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-inequality-theorem-300x164.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about the exterior angle theorem, its statement and proof. We also learned the exterior angle inequality theorem. Let\u2019s solve a few examples and practice problems based on these concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples-on-exterior-angle-theorem\">Solved Examples on Exterior Angle Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Find the value of <\/strong>$\\angle ACB$ <strong>in the following figure.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"279\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/finding-missing-angle-using-exterior-angle-theorem.png\" alt=\"Finding missing angle using exterior angle theorem\" class=\"wp-image-37489\" style=\"width:229px;height:280px\" title=\"Finding missing angle using exterior angle theorem\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle CAD$ is the exterior angle of $\\Delta ABC$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By the exterior angle theorem,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle CAD = \\angle ABC + \\angle ACB$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$120^\\circ = 40^\\circ + \\angle ACB$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle ACB = 120^\\circ \\;-\\; 40^\\circ = 80^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Find the value of <\/strong><strong>x<\/strong><strong> in the following figure.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"249\" height=\"197\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/exterior-angle-theorem-example-involving-angles-with-variables.png\" alt=\"Exterior angle theorem example involving angles with variables\" class=\"wp-image-37490\" title=\"Exterior angle theorem example involving angles with variables\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(8x + 25)^\\circ$ is the exterior angle of $\\Delta PQR$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Its remote interior angles are $(2x + 10)^\\circ$ and $(5x + 20)^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By the exterior angle theorem,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$8x + 25 = 2x + 10 + 5x + 20$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$8x\\;-\\;2x\\;-\\;5x = 10 + 20\\;-\\;25$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x=5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Find the value of <\/strong><strong>y<\/strong><strong> in the following figure.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"270\" height=\"230\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/composite-figure-formed-by-two-triangles.png\" alt=\"Composite figure formed by two triangles\" class=\"wp-image-37491\" title=\"Composite figure formed by two triangles\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">There are two triangles in the figure,<strong> <\/strong>$\\Delta DBC$ and $\\Delta ABE$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle EBA = x$ is the exterior angle of $\\Delta DBC$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By the exterior angle theorem,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle EBA = \\angle BDC + \\angle BCD$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = 30^\\circ + 50^\\circ = 80^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = 80^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle DEA = y$ is the exterior angle of $\\Delta ABE$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By the exterior angle theorem,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle DEA = \\angle EBA + \\angle BAE$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = x + 30^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = 80^\\circ + 30^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y = 110^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Find the value of <\/strong>$\\angle PRQ$ <strong>using exterior angle theorem.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"248\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/two-exterior-angles-of-a-triangle-measuring-110degree-and-135-degree.png\" alt=\"Two exterior angles of a triangle measuring 110\u00b0 and 135\u00b0\" class=\"wp-image-37492\" title=\"Two exterior angles of a triangle measuring 110\u00b0 and 135\u00b0\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">QS is a straight line.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle SPR + \\angle QPR = 180^\\circ$ (Angles in a linear pair.)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$135^\\circ + \\angle QPR = 180^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle QPR = 180^\\circ \\;-\\; 135^\\circ = 45^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle TQP$ is the exterior angle of $\\Delta PQR$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By the exterior angle theorem,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle TQP = \\angle PRQ + \\angle QPR$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$110^\\circ =\\angle PRQ  + 45^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle PRQ = 65^\\circ$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems-on-exterior-angle-theorem\">Practice Problems on Exterior Angle Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Exterior Angle Theorem: Definition, Proof, Examples, Facts, 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\">What will be the value of x 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\/04\/finding-the-measure-of-exterior-angle-of-a-triangle-a-120-degree.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$120^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$100^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$60^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$20^\\circ$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $120^\\circ$<br\/>x is the exterior angle of the triangle.<br>\r\nBy the exterior angle theorem,<br>\r\n$x = 50^\\circ + 70^\\circ = 120^\\circ$<\/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\">The exterior angle of a triangle equals the sum of __________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">interior angles<\/div><div class=\"spq_answer_block\" data-value=\"1\">exterior angles<\/div><div class=\"spq_answer_block\" data-value=\"2\">remote interior angles<\/div><div class=\"spq_answer_block\" data-value=\"3\">any two interior angles<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: remote interior angles<br\/>An exterior angle of a triangle equals the sum of remote interior angles.<\/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\">Find the value of x 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\/04\/example-on-exterior-angle-theorem.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$24^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$54^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$46^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$47^\\circ$<\/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: $47^\\circ$<br\/>In $\\Delta ABC,\\; AB = BC\\Rightarrow  \\angle BAC = \\angle BCA = y$ <br>\r\nBy Angle Sum Property of a Triangle,<br>\r\n$y + y + 50^\\circ = 180^\\circ$<br>\r\n$2y = 130^\\circ$<br>\r\n$y = 65^\\circ$<br>\r\n$\\angle ACB = y$ is the exterior angle of $\\Delta ACD$.<br>\r\n$y = \\angle CAD + \\angle CDA$<br>\r\n$65 = x + 28^\\circ$<br>\r\n$x = 37^\\circ$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What will be the value of each exterior angle of an equilateral triangle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$60^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$120^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$150^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$70^\\circ$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $120^\\circ$<br\/>Each interior angle of an equilateral triangle is $60^\\circ$.<br>\r\nExterior angle $= 60^\\circ + 60^\\circ = 120^\\circ$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Exterior Angle Theorem: Definition, Proof, Examples, Facts, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n  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                               \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$100^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"x is the exterior angle of the triangle.<br>\r\nBy the exterior angle theorem,<br>\r\n$$x = 50^\\\\circ + 70^\\\\circ = 120^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$60^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    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__________.\",\n                    \"text\": \"The exterior angle of a triangle equals the sum of __________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"An exterior angle of a triangle equals the sum of remote interior angles.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"interior angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"An exterior angle of a triangle equals the sum of remote interior angles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"exterior angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"An exterior angle of a triangle equals the sum of remote interior angles.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"any two interior angles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"An exterior angle of a triangle equals the sum of remote interior angles.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"remote interior angles\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"An exterior angle of a triangle equals the sum of remote interior angles.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"An exterior angle of a triangle equals the sum of remote interior angles.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the value of x in the following figure.\",\n                    \"text\": \"Find the value of x in the following figure. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/example-on-exterior-angle-theorem.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In $$\\\\Delta ABC,\\\\; AB = BC\\\\Rightarrow  \\\\angle BAC = \\\\angle BCA = y$$ <br>\r\nBy Angle Sum Property of a Triangle,<br>\r\n$$y + y + 50^\\\\circ = 180^\\\\circ$$<br>\r\n$$2y = 130^\\\\circ$$<br>\r\n$$y = 65^\\\\circ$$<br>\r\n$$\\\\angle ACB = y$$ is the exterior angle of $$\\\\Delta ACD$$.<br>\r\n$$y = \\\\angle CAD + \\\\angle CDA$$<br>\r\n$$65 = x + 28^\\\\circ$$<br>\r\n$$x = 37^\\\\circ$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$24^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In $$\\\\Delta ABC,\\\\; AB = BC\\\\Rightarrow  \\\\angle BAC = \\\\angle BCA = y$$ <br>\r\nBy Angle Sum Property of a Triangle,<br>\r\n$$y + y + 50^\\\\circ = 180^\\\\circ$$<br>\r\n$$2y = 130^\\\\circ$$<br>\r\n$$y = 65^\\\\circ$$<br>\r\n$$\\\\angle ACB = y$$ is the exterior angle of $$\\\\Delta ACD$$.<br>\r\n$$y = \\\\angle CAD + \\\\angle CDA$$<br>\r\n$$65 = x + 28^\\\\circ$$<br>\r\n$$x = 37^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$54^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In $$\\\\Delta ABC,\\\\; AB = BC\\\\Rightarrow  \\\\angle BAC = \\\\angle BCA = y$$ <br>\r\nBy Angle Sum Property of a Triangle,<br>\r\n$$y + y + 50^\\\\circ = 180^\\\\circ$$<br>\r\n$$2y = 130^\\\\circ$$<br>\r\n$$y = 65^\\\\circ$$<br>\r\n$$\\\\angle ACB = y$$ is the exterior angle of $$\\\\Delta ACD$$.<br>\r\n$$y = \\\\angle CAD + \\\\angle CDA$$<br>\r\n$$65 = x + 28^\\\\circ$$<br>\r\n$$x = 37^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$46^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In $$\\\\Delta ABC,\\\\; AB = BC\\\\Rightarrow  \\\\angle BAC = \\\\angle BCA = y$$ <br>\r\nBy Angle Sum Property of a Triangle,<br>\r\n$$y + y + 50^\\\\circ = 180^\\\\circ$$<br>\r\n$$2y = 130^\\\\circ$$<br>\r\n$$y = 65^\\\\circ$$<br>\r\n$$\\\\angle ACB = y$$ is the exterior angle of $$\\\\Delta ACD$$.<br>\r\n$$y = \\\\angle CAD + \\\\angle CDA$$<br>\r\n$$65 = x + 28^\\\\circ$$<br>\r\n$$x = 37^\\\\circ$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$47^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In $$\\\\Delta ABC,\\\\; AB = BC\\\\Rightarrow  \\\\angle BAC = \\\\angle BCA = y$$ <br>\r\nBy Angle Sum Property of a Triangle,<br>\r\n$$y + y + 50^\\\\circ = 180^\\\\circ$$<br>\r\n$$2y = 130^\\\\circ$$<br>\r\n$$y = 65^\\\\circ$$<br>\r\n$$\\\\angle ACB = y$$ is the exterior angle of $$\\\\Delta ACD$$.<br>\r\n$$y = \\\\angle CAD + \\\\angle CDA$$<br>\r\n$$65 = x + 28^\\\\circ$$<br>\r\n$$x = 37^\\\\circ$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In $$\\\\Delta ABC,\\\\; AB = BC\\\\Rightarrow  \\\\angle BAC = \\\\angle BCA = y$$ <br>\r\nBy Angle Sum Property of a Triangle,<br>\r\n$$y + y + 50^\\\\circ = 180^\\\\circ$$<br>\r\n$$2y = 130^\\\\circ$$<br>\r\n$$y = 65^\\\\circ$$<br>\r\n$$\\\\angle ACB = y$$ is the exterior angle of $$\\\\Delta ACD$$.<br>\r\n$$y = \\\\angle CAD + \\\\angle CDA$$<br>\r\n$$65 = x + 28^\\\\circ$$<br>\r\n$$x = 37^\\\\circ$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What will be the value of each exterior angle of an equilateral triangle?\",\n                    \"text\": \"What will be the value of each exterior angle of an equilateral triangle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Each interior angle of an equilateral triangle is $$60^\\\\circ$$.<br>\r\nExterior angle $$= 60^\\\\circ + 60^\\\\circ = 120^\\\\circ$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$60^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Each interior angle of an equilateral triangle is $$60^\\\\circ$$.<br>\r\nExterior angle $$= 60^\\\\circ + 60^\\\\circ = 120^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$150^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Each interior angle of an equilateral triangle is $$60^\\\\circ$$.<br>\r\nExterior angle $$= 60^\\\\circ + 60^\\\\circ = 120^\\\\circ$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$70^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Each interior angle of an equilateral triangle is $$60^\\\\circ$$.<br>\r\nExterior angle $$= 60^\\\\circ + 60^\\\\circ = 120^\\\\circ$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$120^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Each interior angle of an equilateral triangle is $$60^\\\\circ$$.<br>\r\nExterior angle $$= 60^\\\\circ + 60^\\\\circ = 120^\\\\circ$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Each interior angle of an equilateral triangle is $$60^\\\\circ$$.<br>\r\nExterior angle $$= 60^\\\\circ + 60^\\\\circ = 120^\\\\circ$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions-on-exterior-angle-theorem\">Frequently Asked Questions on Exterior Angle Theorem<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-59d6052b-d318-41ad-8553-cbfe26e060ab\" 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-0-59d6052b-d318-41ad-8553-cbfe26e060ab\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-59d6052b-d318-41ad-8553-cbfe26e060ab\"><strong>Why is the sum of exterior angles of a triangle is <\/strong>$360^\\circ$<strong>?<\/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-0-59d6052b-d318-41ad-8553-cbfe26e060ab\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The sum of angles in a triangle is $180^\\circ$. Each exterior angle of a triangle equals the sum of two remote interior angles. If we add the three exterior angles, we will have to add each interior angle twice. Thus, the sum of the measures of the exterior angles of a triangle is $360^\\circ$ degrees.<\/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-1-59d6052b-d318-41ad-8553-cbfe26e060ab\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-59d6052b-d318-41ad-8553-cbfe26e060ab\"><strong>What is the difference between angle sum property of a triangle and exterior angle property of a triangle?<\/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-1-59d6052b-d318-41ad-8553-cbfe26e060ab\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the angle sum property of a triangle, the sum of all the interior angles of a triangle equals $180^\\circ$. On the other hand, the exterior angle theorem states that exterior angle is equal to the sum of remote interior angles.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-59d6052b-d318-41ad-8553-cbfe26e060ab\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-59d6052b-d318-41ad-8553-cbfe26e060ab\"><strong>If each interior angle of a triangle gets doubled, then how will it affect the exterior angle of the triangle?<\/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-2-59d6052b-d318-41ad-8553-cbfe26e060ab\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If each interior angle of a triangle gets doubled, then the exterior angle of the triangle gets doubled.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Original equation for the exterior angle \u201ce\u201d: $e = a + b$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">New equation: $e = 2a + 2b = 2(a+b) = 2e$<\/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-3-59d6052b-d318-41ad-8553-cbfe26e060ab\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-59d6052b-d318-41ad-8553-cbfe26e060ab\"><strong>How many exterior angles does a triangle have?<\/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-3-59d6052b-d318-41ad-8553-cbfe26e060ab\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A triangle has 6 exterior angles.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-59d6052b-d318-41ad-8553-cbfe26e060ab\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-59d6052b-d318-41ad-8553-cbfe26e060ab\"><strong>What is the exterior angle theorem formula?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-59d6052b-d318-41ad-8553-cbfe26e060ab\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Exterior Angle $=$ The sum of two remote (opposite) interior angles<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Exterior Angle Theorem? Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles. The remote interior angles or opposite interior angles are the angles that are non-adjacent with the exterior angle. A triangle is a polygon with three &#8230; <a title=\"Exterior Angle Theorem: Definition, Proof, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/exterior-angle-theorem\" aria-label=\"More on Exterior Angle Theorem: Definition, Proof, Examples, Facts, 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-28113","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\/28113","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=28113"}],"version-history":[{"count":14,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28113\/revisions"}],"predecessor-version":[{"id":39879,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28113\/revisions\/39879"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=28113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=28113"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=28113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}