{"id":26557,"date":"2023-03-20T09:16:27","date_gmt":"2023-03-20T09:16:27","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26557"},"modified":"2024-02-05T16:16:12","modified_gmt":"2024-02-05T16:16:12","slug":"angle-sum-property-of-a-triangle-definition-theorem-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/angle-sum-theorem","title":{"rendered":"Angle Sum Property of a Triangle: Definition, Theorem, Examples"},"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-18f1ddb3-6c54-4d53-9eb9-9610a4c52159\" 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\/angle-sum-theorem#0-what-is-the-angle-sum-property-of-a-triangle>What is the Angle Sum Property of a Triangle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angle-sum-theorem#2-triangle-sum-theorem-proof>Triangle Sum Theorem Proof<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angle-sum-theorem#3-exterior-angle-theorem>Exterior Angle Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angle-sum-theorem#6-solved-examples-on-angle-sum-property-of-a-triangle>Solved Examples on Angle Sum Property of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angle-sum-theorem#7-practice-problems-on-angle-sum-property-of-a-triangle>Practice Problems on Angle Sum Property of a Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/angle-sum-theorem#8-frequently-asked-questions-on-angle-sum-property-of-a-triangle>Frequently Asked Questions on Angle Sum Property of a Triangle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-angle-sum-property-of-a-triangle\">What is the Angle Sum Property of a Triangle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The \u201cangle sum property of a triangle theorem\u201d (also known as the \u201ctriangle sum theorem\u201d or \u201cangle sum theorem\u201d) states that the <strong>sum of the three interior angles of any triangle is always <\/strong>$180^{\\circ}$<strong>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"380\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angle-sum-property-visual.png\" alt=\"Angle sum property visual\" class=\"wp-image-33764\" title=\"Angle sum property visual\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angle-sum-property-visual.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angle-sum-property-visual-300x184.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">What is the angle sum theorem in geometry? <strong>In Euclidean geometry, any triangle whether it is a right triangle, an obtuse triangle, or an acute triangle all have interior angles that add up to 180 degrees<\/strong>.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-and-mark-the-sum-on-the-number-line\" 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\/add_sub_facts_where_sum_pt.png\" alt=\"Add and Mark the Sum on the Number Line 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 and Mark the Sum on the Number Line 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\/add-and-match-to-find-the-sum\" 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\/add_sub_facts_add_and_match_2_pt.png\" alt=\"Add and Match to Find the Sum 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 and Match to Find the Sum 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\/add-like-fractions-to-get-a-sum-greater-than-1\" 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\/fractions_add_like_frac_sum_greater_than_1_pt.png\" alt=\"Add Like Fractions to Get a Sum Greater than 1 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 Like Fractions to Get a Sum Greater than 1 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\/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\/add-to-find-the-sum\" 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\/add_sub_pv_add_num_1_pt.png\" alt=\"Add to Find the Sum 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 to Find the Sum 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\/choose-the-correct-sum\" 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\/rec_add_sub_facts_find_missing_sum_4_pt.png\" alt=\"Choose the Correct Sum 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\">Choose the Correct Sum 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\/choose-the-sum-of-the-mixed-number-and-the-fraction\" 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\/fractions_add_mixed_num_and_frac_models_pt.png\" alt=\"Choose the Sum of the Mixed Number and the Fraction 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\">Choose the Sum of the Mixed Number and the Fraction 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><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-angle-sum-property-of-a-triangle-theorem\">Angle Sum Property of a Triangle Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The angle sum property of a triangle theorem states that the sum of all three internal angles of a triangle is $180^{\\circ}$. It is also known as the <strong>angle sum theorem<\/strong> or<strong> triangle sum theorem<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"489\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/triangle-sum-theorem-visual.png\" alt=\"Triangle sum theorem visual\" class=\"wp-image-33765\" title=\"Triangle sum theorem visual\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/triangle-sum-theorem-visual.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/triangle-sum-theorem-visual-300x237.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the angle sum theorem, in the above ABC,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle A + m\\angle B + m\\angle C = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example<\/strong>: In PQR, $\\angle P = 60^{\\circ}, \\angle Q = 70^{\\circ}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"381\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angle-sum-property-of-triangle.png\" alt=\"Angle sum property of triangle\" class=\"wp-image-33766\" title=\"Angle sum property of triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angle-sum-property-of-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/angle-sum-property-of-triangle-300x184.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the angle sum theorem, in the above triangle PQR,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle P + m\\angle Q + m\\angle R = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$60^{\\circ} + 70^{\\circ} + m\\angle R = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$130^{\\circ} + m\\angle R = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$m\\angle R = 50^{\\circ}$<\/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\/add-1-digit-and-3-digit-numbers-and-find-the-sum\" 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\/add-1-digit-and-3-digit-numbers-and-find-the-sum.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers and Find the Sum\">\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\/add-1-digit-and-3-digit-numbers-and-match-the-sum\" 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\/add-1-digit-and-3-digit-numbers-and-match-the-sum.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers and Match the Sum\">\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\/add-100-and-find-the-sum\" 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\/add-100-and-find-the-sum.jpeg\" alt=\"Add 100 and Find the Sum\">\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\/add-100-and-match-the-sum\" 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\/add-100-and-match-the-sum.jpeg\" alt=\"Add 100 and Match the Sum\">\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\/add-3-numbers-within-10-summer-word-problems\" 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\/add-3-numbers-within-10-summer-word-problems.jpeg\" alt=\"Add 3 Numbers within 10: Summer Word Problems\">\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\/add-3-numbers-within-100-summer-word-problems\" 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\/add-3-numbers-within-100-summer-word-problems.jpeg\" alt=\"Add 3 Numbers within 100: Summer Word Problems\">\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 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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                   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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-triangle-sum-theorem-proof\">Triangle Sum Theorem Proof<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the figure given below, AB, BC, and CA represent three sides of triangle ABC. A, B, and C are the three vertices. $\\angle A,\\; \\angle B,$ and $\\angle C$ are the three interior angles of $\\Delta ABC$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"293\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/triangle-sum-theorem-proof.png\" alt=\"Triangle sum theorem proof\" class=\"wp-image-33767\" title=\"Triangle sum theorem proof\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/triangle-sum-theorem-proof.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/triangle-sum-theorem-proof-300x142.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In \u2206ABC, we have to prove that the sum of the angles $\\angle A,\\; \\angle B,$ and $\\angle C$ is $180^{\\circ}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>To prove:<\/strong> $m\\angle A + m \\angle B + m\\angle C = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Construction:<\/strong> Draw a line DE passing through the vertex B, which is parallel to the side AC.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">At point B, two angles are formed, $\\angle 1$ and $\\angle 2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since AB is a transversal for the parallel lines DE and AC, we have&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle 1 = m\\angle A$ (since the pair of alternate interior angles are equal)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly, $m\\angle 2 = m\\angle C$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, $m\\angle 1,\\; m\\angle B,$ and $m\\angle 2$ must add up to $180^{\\circ}$ (angles on a straight line).&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $\\angle 1 + \\angle B + \\angle 2 = 180^{\\circ}$\u2026 (I)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since $\\angle 1 = \\angle A$ and $\\angle 2 = \\angle C$. \u2026 (II)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Substituting equation (II) in equation (I), we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle A + m\\angle B + m\\angle C = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, the sum of the three angles $\\angle A,\\; \\angle B,$ and $\\angle C$ is $180^{\\circ}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, the triangle sum theorem was proved.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-exterior-angle-theorem\">Exterior Angle Theorem<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The exterior angle theorem states that \u201can exterior angle of a triangle is equal to the sum of its two opposite interior angles.\u201d<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"466\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/exterior-angle-property-of-triangle.png\" alt=\"Exterior angle property of triangle\" class=\"wp-image-33768\" title=\"Exterior angle property of triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/exterior-angle-property-of-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/exterior-angle-property-of-triangle-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the above triangle, $\\angle A,\\; \\angle B,$ and $\\angle C$ are the interior angles of the triangle ABC, and $\\angle 1,\\; \\angle 2,$ and $\\angle 3$ are the exterior angle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle A + m\\angle B + m\\angle C = 180^{\\circ}$ (angle sum property) \u2026 (I)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Also, $m\\angle A + m\\angle 1 = 180^{\\circ}$ (linear pair angle) \u2026 (II)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">From (I) and (II), we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle A + m\\angle 1 = m\\angle A + m\\angle B + m\\angle C$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle 1 = m\\angle B + m\\angle C$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Similarly, we can derive for other two exterior angles,\u22202 and \u22203 which is given by:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle 2 = m\\angle A + m\\angle C$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle 3 = m\\angle A + m\\angle B$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>In summary:&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"406\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/exterior-angle-theorem.png\" alt=\"Exterior angle theorem\" class=\"wp-image-33769\" title=\"Exterior angle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/exterior-angle-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/exterior-angle-theorem-300x196.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-facts-about-angle-sum-property-of-a-triangle\">Facts about Angle Sum Property of a Triangle<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The theorem of angle sum property of triangles holds true for all types of triangles.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The sum of all exterior angles of a triangle is equal to $360^{\\circ}$.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The sum of the lengths of any two sides of a triangle is always greater than the third side.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">A rectangle can be divided into two right triangles by drawing a line from one corner to the opposite corner.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The study of the relationship between the sides and angles of triangles is known as trigonometry.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Due to their high strength, triangle shapes are frequently utilized in construction.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">In North Carolina, there are three cities: Raleigh, Durham, and Chapel Hill, that are often referred to as the triangle.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The sum of all exterior angles of a triangle is equal to $360^{\\circ}$.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we have learned all about the angle sum property of a triangle, exterior angle property of a triangle, proof of triangle sum theorem, and some important facts about triangles.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s solve a few triangle angle sum theorem examples and practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-solved-examples-on-angle-sum-property-of-a-triangle\">Solved Examples on Angle Sum Property of a Triangle<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>In a triangle, ABC, if <\/strong>$m\\angle A = 60^{\\circ},\\; m\\angle B = 40^{\\circ}$<strong>, then find the measure of angle <\/strong>$\\angle C$<strong>.<\/strong><\/li>\n<\/ol>\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\">In $\\Delta ABC,\\; \\angle A = 60^{\\circ}$ and $\\angle B = 40^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the sum of angles in a triangle is $180^{\\circ}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow&nbsp; m \\angle A + \\angle B + \\angle C = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow&nbsp; 60^{\\circ} + 40^{\\circ} + \\angle C = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow&nbsp; \\angle C = 180^{\\circ} \\;\u2212\\; ( 60^{\\circ} + 40^{\\circ})$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow&nbsp; \\angle C = 180^{\\circ} \\;\u2212\\; 100^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\therefore&nbsp; \\angle C = 80^{\\circ}$<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>One of the acute angles in a right-angled triangle is <\/strong>$40^{\\circ}$<strong>. Using the angle sum theorem, determine the other angle.&nbsp;<\/strong><\/li>\n<\/ol>\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\">Let $\\Delta ABC$ be given a right-angled triangle which is right-angled at B.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\therefore&nbsp; \\angle B = 90^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$m\\angle A = 40^{\\circ}$ and we have to find out $m\\angle C$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the sum of angles in a triangle is $180^{\\circ}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow&nbsp; m \\angle A + m \\angle B + m \\angle C = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow&nbsp; 40^{\\circ} +&nbsp; 90^{\\circ} + m\\angle C = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow&nbsp; m \\angle C = 180^{\\circ} \\;\u2212\\; (40^{\\circ} + 90^{\\circ})$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow&nbsp; m \\angle C = 180^{\\circ} \\;\u2212\\; 130^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\therefore&nbsp; m \\angle C = 50^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\therefore m \\angle A = m \\angle C = 50^{\\circ}$<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>The measures of interior angles of a triangle are <\/strong>$(2x\\;\u2212\\;20)^{\\circ}, (3x\\;\u2212\\;10)^{\\circ}$<sup>,<\/sup><strong> and <\/strong>$2x^{\\circ}$<strong>, find the values of all three angles of the triangle.<\/strong><\/li>\n<\/ol>\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\">We know that the sum of angles in a triangle is $180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow (2x\\;\u2212\\;20)^{\\circ} + (3x\\;\u2212\\;10)^{\\circ} + 2x^{\\circ} = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow (2x\\;\u2212\\;20 + 3x\\;\u2212\\;10 + 2x)^{\\circ} = 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow 7x\\;\u2212\\;30 = 180$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow 7x = 180 + 30$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow 7x = 210$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow x = 2107= 30$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow$ Angles are $40^{\\circ},\\; 80^{\\circ}$ and $60^{\\circ}$.<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Is it possible to construct a triangle with internal angles <\/strong>$43^{\\circ},\\; 49^{\\circ},$<strong> and <\/strong>$91^{\\circ}$<strong>?<\/strong><\/li>\n<\/ol>\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\">Given, measurements of angles<strong> <\/strong>$43^{\\circ},\\; 49^{\\circ},$<strong> and <\/strong>$91^{\\circ}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, $43^{\\circ} + 49^{\\circ} + 91^{\\circ} = 183^{\\circ} 180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know, that, the sum of angles in a triangle is $180^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, it is not possible to construct a triangle with measurements of angles $43^{\\circ},\\; 49^{\\circ},$ and $91^{\\circ}$.<\/p>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>In the figure given below, determine the value of \u201cx.\u201d<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"283\" height=\"202\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/09\/example-on-angle-sum-property-of-triangle.png\" alt=\"Example on angle sum property of triangle\" class=\"wp-image-33770\" title=\"Example on angle sum property of triangle\"\/><\/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\">In the above figure, $\\angle x$ is an exterior angle and $\\angle A = 55^{\\circ}$ and $\\angle B = 47^{\\circ}$ are given as interior angles.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the exterior angle property,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">an exterior angle of a triangle is equal to the sum of its two interior opposite angles.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">So, $\\angle x = \\angle A + \\angle B = 55^{\\circ} + 47^{\\circ} = 102^{\\circ}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Hence, $x = 102^{\\circ}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-practice-problems-on-angle-sum-property-of-a-triangle\">Practice Problems on Angle Sum Property of a Triangle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Angle Sum Property of a Triangle: Definition, Theorem, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">If all angles of a triangle are congruent, then each angle measures ___.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$80^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$40^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$60^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$50^{\\circ}$<\/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\/>Sum of all angles of a triangle is $180^{\\circ}$. If all angles of a triangle are congruent, then we have<br>\r\n$3x = 180^{\\circ}$. Thus, $x = 60^{\\circ}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the sum of all interior angles of a triangle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$60^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$90^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$120^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$180^{\\circ}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $180^{\\circ}$<br\/>According to the angle sum theorem the sum of all three internal angles of a triangle is $180^{\\circ}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Two angles of a triangle measure $30^{\\circ}$ and $60^{\\circ}$. The measure of the third angle is _____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$30^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$90^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$130^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$180^{\\circ}$<\/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: $90^{\\circ}$<br\/>We know that the sum of angles in a triangle is $180^{\\circ}$.<br>\r\nThus, the measure of the third angle $= 180^{\\circ} \\;\u2212\\; (30^{\\circ} + 60^{\\circ}) = 90^{\\circ}$<\/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\">Find x.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/applying-the-exterior-angle-theorem.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$100^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$109^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$105^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$104^{\\circ}$<\/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: $109^{\\circ}$<br\/>Exterior angle property of a triangle states that \u201can exterior angle of a triangle is equal to the sum of its two interior opposite angles.\u201d\r\nThus, $x = 109^{\\circ}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">What is the sum of all exterior angles of a triangle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$90^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$180^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$270^{\\circ}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$360^{\\circ}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $360^{\\circ}$<br\/>Each exterior angle is the sum of its two opposite interior angles. Thus, the sum of all the exterior angles is two times the sum of all interior angles. The sum of all exterior angles of a triangle is equal to $360^{\\circ}$.<\/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\": \"Angle Sum Property of a Triangle: Definition, Theorem, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Angle Sum Property of a Triangle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If all angles of a triangle are congruent, then each angle measures ___.\",\n                    \"text\": \"If all angles of a triangle are congruent, then each angle measures ___.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Sum of all angles of a triangle is $$180^{\\\\circ}$$. If all angles of a triangle are congruent, then we have<br>\r\n$$3x = 180^{\\\\circ}$$. Thus, $$x = 60^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$80^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sum of all angles of a triangle is $$180^{\\\\circ}$$. If all angles of a triangle are congruent, then we have<br>\r\n$$3x = 180^{\\\\circ}$$. Thus, $$x = 60^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$40^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sum of all angles of a triangle is $$180^{\\\\circ}$$. If all angles of a triangle are congruent, then we have<br>\r\n$$3x = 180^{\\\\circ}$$. Thus, $$x = 60^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$50^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Sum of all angles of a triangle is $$180^{\\\\circ}$$. If all angles of a triangle are congruent, then we have<br>\r\n$$3x = 180^{\\\\circ}$$. Thus, $$x = 60^{\\\\circ}$$.\"\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\": \"Sum of all angles of a triangle is $$180^{\\\\circ}$$. If all angles of a triangle are congruent, then we have<br>\r\n$$3x = 180^{\\\\circ}$$. Thus, $$x = 60^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Sum of all angles of a triangle is $$180^{\\\\circ}$$. If all angles of a triangle are congruent, then we have<br>\r\n$$3x = 180^{\\\\circ}$$. Thus, $$x = 60^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the sum of all interior angles of a triangle?\",\n                    \"text\": \"What is the sum of all interior angles of a triangle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the angle sum theorem the sum of all three internal angles of a triangle is $$180^{\\\\circ}$$.\"\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\": \"According to the angle sum theorem the sum of all three internal angles of a triangle is $$180^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$90^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the angle sum theorem the sum of all three internal angles of a triangle is $$180^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$120^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the angle sum theorem the sum of all three internal angles of a triangle is $$180^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$180^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the angle sum theorem the sum of all three internal angles of a triangle is $$180^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the angle sum theorem the sum of all three internal angles of a triangle is $$180^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Two angles of a triangle measure $$30^{\\\\circ}$$ and $$60^{\\\\circ}$$. The measure of the third angle is _____.\",\n                    \"text\": \"Two angles of a triangle measure $$30^{\\\\circ}$$ and $$60^{\\\\circ}$$. The measure of the third angle is _____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that the sum of angles in a triangle is $$180^{\\\\circ}$$.<br>\r\nThus, the measure of the third angle $$= 180^{\\\\circ} \\\\;\u2212\\\\; (30^{\\\\circ} + 60^{\\\\circ}) = 90^{\\\\circ}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$30^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the sum of angles in a triangle is $$180^{\\\\circ}$$.<br>\r\nThus, the measure of the third angle $$= 180^{\\\\circ} \\\\;\u2212\\\\; (30^{\\\\circ} + 60^{\\\\circ}) = 90^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$130^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the sum of angles in a triangle is $$180^{\\\\circ}$$.<br>\r\nThus, the measure of the third angle $$= 180^{\\\\circ} \\\\;\u2212\\\\; (30^{\\\\circ} + 60^{\\\\circ}) = 90^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$180^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the sum of angles in a triangle is $$180^{\\\\circ}$$.<br>\r\nThus, the measure of the third angle $$= 180^{\\\\circ} \\\\;\u2212\\\\; (30^{\\\\circ} + 60^{\\\\circ}) = 90^{\\\\circ}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$90^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that the sum of angles in a triangle is $$180^{\\\\circ}$$.<br>\r\nThus, the measure of the third angle $$= 180^{\\\\circ} \\\\;\u2212\\\\; (30^{\\\\circ} + 60^{\\\\circ}) = 90^{\\\\circ}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that the sum of angles in a triangle is $$180^{\\\\circ}$$.<br>\r\nThus, the measure of the third angle $$= 180^{\\\\circ} \\\\;\u2212\\\\; (30^{\\\\circ} + 60^{\\\\circ}) = 90^{\\\\circ}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find x.\",\n                    \"text\": \"Find x. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/applying-the-exterior-angle-theorem.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Exterior angle property of a triangle states that \u201can exterior angle of a triangle is equal to the sum of its two interior opposite angles.\u201d\r\nThus, $$x = 109^{\\\\circ}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$100^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Exterior angle property of a triangle states that \u201can exterior angle of a triangle is equal to the sum of its two interior opposite angles.\u201d\r\nThus, $$x = 109^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$105^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Exterior angle property of a triangle states that \u201can exterior angle of a triangle is equal to the sum of its two interior opposite angles.\u201d\r\nThus, $$x = 109^{\\\\circ}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$104^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Exterior angle property of a triangle states that \u201can exterior angle of a triangle is equal to the sum of its two interior opposite angles.\u201d\r\nThus, $$x = 109^{\\\\circ}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$109^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Exterior angle property of a triangle states that \u201can exterior angle of a triangle is equal to the sum of its two interior opposite angles.\u201d\r\nThus, $$x = 109^{\\\\circ}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Exterior angle property of a triangle states that \u201can exterior angle of a triangle is equal to the sum of its two interior opposite angles.\u201d\r\nThus, $$x = 109^{\\\\circ}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the sum of all exterior angles of a triangle?\",\n                    \"text\": \"What is the sum of all exterior angles of a triangle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Each exterior angle is the sum of its two opposite interior angles. Thus, the sum of all the exterior angles is two times the sum of all interior angles. The sum of all exterior angles of a triangle is equal to $$360^{\\\\circ}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$90^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Each exterior angle is the sum of its two opposite interior angles. Thus, the sum of all the exterior angles is two times the sum of all interior angles. The sum of all exterior angles of a triangle is equal to $$360^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$180^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Each exterior angle is the sum of its two opposite interior angles. Thus, the sum of all the exterior angles is two times the sum of all interior angles. The sum of all exterior angles of a triangle is equal to $$360^{\\\\circ}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$270^{\\\\circ}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Each exterior angle is the sum of its two opposite interior angles. Thus, the sum of all the exterior angles is two times the sum of all interior angles. The sum of all exterior angles of a triangle is equal to $$360^{\\\\circ}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$360^{\\\\circ}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Each exterior angle is the sum of its two opposite interior angles. Thus, the sum of all the exterior angles is two times the sum of all interior angles. The sum of all exterior angles of a triangle is equal to $$360^{\\\\circ}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Each exterior angle is the sum of its two opposite interior angles. Thus, the sum of all the exterior angles is two times the sum of all interior angles. The sum of all exterior angles of a triangle is equal to $$360^{\\\\circ}$$.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-frequently-asked-questions-on-angle-sum-property-of-a-triangle\">Frequently Asked Questions on Angle Sum Property of a Triangle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\" 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-0-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\"><strong>What is the difference between the angle sum theorem and the exterior angle theorem?<\/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-0-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The angle sum theorem states that the sum of all three internal angles of a triangle is 180\u00b0. Whereas the exterior angle theorem states that an exterior angle of a triangle is equal to the sum of its two interior opposite 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-1-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\"><strong>Can we define the angle sum property for a quadrilateral?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, we can define the angle sum property for a quadrilateral. According to the angle sum property of a quadrilateral, the sum of all four interior angles is 360 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-2-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\"><strong>What is the sum of all exterior angles of a quadrilateral?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The sum of all exterior angles of any polygon is equal to $360^{\\circ}$. Hence the sum of all exterior angles of a quadrilateral is also equal to $360^{\\circ}$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\"><strong>What is the formula for the angle sum 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-3-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the sum of angles in a triangle is $180^{\\circ}$. For $\\Delta ABC$, the formula for the angle sum property of a triangle is $\\angle A + \\angle B + \\angle C = 180^{\\circ}$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\"><strong>What Is the angle sum theorem for any polygon?<\/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-4-87c3a177-e2e5-4c6f-9e14-296fa0b2016e\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the angle sum theorem for any polygon, the sum of all interior angles is equal to&nbsp;$(n \u2212 2) \\times 180^{\\circ}$, where n is the total number of sides of the polygon.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What is the Angle Sum Property of a Triangle? The \u201cangle sum property of a triangle theorem\u201d (also known as the \u201ctriangle sum theorem\u201d or \u201cangle sum theorem\u201d) states that the sum of the three interior angles of any triangle is always $180^{\\circ}$. What is the angle sum theorem in geometry? In Euclidean geometry, any &#8230; <a title=\"Angle Sum Property of a Triangle: Definition, Theorem, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/angle-sum-theorem\" aria-label=\"More on Angle Sum Property of a Triangle: Definition, Theorem, Examples\">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-26557","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\/26557","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=26557"}],"version-history":[{"count":13,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26557\/revisions"}],"predecessor-version":[{"id":39969,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26557\/revisions\/39969"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26557"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26557"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}