{"id":32896,"date":"2023-08-13T16:46:54","date_gmt":"2023-08-13T16:46:54","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=32896"},"modified":"2023-08-13T18:26:31","modified_gmt":"2023-08-13T18:26:31","slug":"vertical-angles-definition-theorem-facts-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/vertical-angles","title":{"rendered":"Vertical Angles &#8211; Definition, Theorem, Facts, 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-419a3058-fffb-4eb5-ab1c-cc35d53b6efb\" 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\/vertical-angles#0-what-are-vertical-angles>What Are Vertical Angles?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertical-angles#5-are-vertical-angles-supplementary>Are Vertical Angles Supplementary?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertical-angles#6-are-vertical-angles-complementary>Are Vertical Angles Complementary?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertical-angles#11-solved-examples-on-vertical-angles>Solved Examples on Vertical Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertical-angles#12-practice-problems-on-vertical-angles>Practice Problems on Vertical Angles<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/vertical-angles#13-frequently-asked-questions-on-vertical-angles>Frequently Asked Questions on Vertical Angles<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-vertical-angles\">What Are Vertical Angles?<\/h2>\n\n\n\n<p>Whenever two lines cross or intersect each other, four angles are formed. Out of these, the angles opposite to each other are called vertical angles or vertically opposite angles. Vertical angles are always congruent.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"342\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-formed-by-intersection-of-two-lines.png\" alt=\"Vertical angles formed by intersection of two lines\" class=\"wp-image-32960\" title=\"Vertical angles formed by intersection of two lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-formed-by-intersection-of-two-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-formed-by-intersection-of-two-lines-300x165.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Here, the pairs of vertical angles are<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u22201 &amp; \u22203<\/li>\n\n\n\n<li>\u22202 &amp; \u22204<\/li>\n<\/ul>\n\n\n\n<p>Observe that the two angles opposite to each other are equal.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-the-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_add_angles_pt.png\" alt=\"Add the Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add the Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-in-multiples-of-10-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_1_pt.png\" alt=\"Draw Angles in Multiples of 10 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles in Multiples of 10 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-nearest-5-and-1-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_2_pt.png\" alt=\"Draw Angles Nearest 5 and 1 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles Nearest 5 and 1 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-using-a-protractor\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_protractor_pt.png\" alt=\"Draw Angles Using a Protractor Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles Using a Protractor Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-right-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_right_angle_1_pt.png\" alt=\"Find Right Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Right Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-perimeter-of-the-squared-and-the-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_rectangle_2_pt.png\" alt=\"Find the Perimeter of the Squared and the Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Perimeter of the Squared and the Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-angles-by-their-types\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_types_of_angle_pt.png\" alt=\"Identify Angles by their Types Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Angles by their Types Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        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                    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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-vertical-angles-definition\">Vertical Angles: Definition<\/h2>\n\n\n\n<p>Vertical angles can be defined as the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/angle\">angles<\/a> that lie opposite to each other when two lines intersect.&nbsp;<\/p>\n\n\n\n<p>Two vertical angles always share a common vertex. However, they never share a common side (arm).<\/p>\n\n\n\n<p>For example, \u2220AOD and \u2220BOC are vertical angles.&nbsp;<\/p>\n\n\n\n<p>They share a common vertex O. However, they do not share a common arm.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"343\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-share-a-common-vertex.png\" alt=\"Vertical angles share a common vertex\" class=\"wp-image-32961\" title=\"Vertical angles share a common vertex\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-share-a-common-vertex.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-share-a-common-vertex-300x166.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/1-and-2-more-within-10-vertical-addition\" 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\/1-and-2-more-within-10-vertical-addition.jpeg\" alt=\"1 and 2 more within 10: Vertical Addition 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\/1-and-2-more-within-20-vertical-addition\" 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\/1-and-2-more-within-20-vertical-addition.jpeg\" alt=\"1 and 2 more within 20: Vertical Addition 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\/add-1-within-10-vertical-addition\" 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-within-10-vertical-addition.jpeg\" alt=\"Add 1 within 10: Vertical Addition 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\/add-1-within-20-vertical-addition\" 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-within-20-vertical-addition.jpeg\" alt=\"Add 1 within 20: Vertical Addition 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\/add-1-within-5-vertical-addition\" 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-within-5-vertical-addition.jpeg\" alt=\"Add 1 within 5: Vertical Addition 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\/add-1-digit-numbers-and-teen-numbers-vertical-addition\" 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-numbers-and-teen-numbers-vertical-addition.jpeg\" alt=\"Add 1-Digit Numbers and Teen Numbers: Vertical Addition 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\/add-10-to-a-3-digit-number-vertical-addition\" 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-10-to-a-3-digit-number-vertical-addition.jpeg\" alt=\"Add 10 to a 3-Digit Number: Vertical Addition 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\/add-10-to-a-3-digit-number-vertical-timed-practice\" 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-10-to-a-3-digit-number-vertical-timed-practice.jpeg\" alt=\"Add 10 to a 3-Digit Number: Vertical Timed Practice\">\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-10-within-20-vertical-addition\" 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-10-within-20-vertical-addition.jpeg\" alt=\"Add 10 within 20: Vertical Addition 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\/add-2-to-numbers-within-10-vertical-addition\" 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-2-to-numbers-within-10-vertical-addition.jpeg\" alt=\"Add 2 to Numbers within 10: Vertical Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-vertical-angles-theorem\">Vertical Angles Theorem<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-e49f74e6-aea9-4551-b199-49ea406e27b3\">\n\n\n<p><strong>Statement: <\/strong>The vertical angles formed when two lines intersect each other are always equal to each other.<\/p>\n\n\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"3-vertical-angles-theorem-proof\">Vertical Angles Theorem: Proof<\/h2>\n\n\n\n<p>To prove: Vertical angles formed when two lines intersect each other are congruent.<\/p>\n\n\n\n<p>Here, we have to prove that&nbsp;<\/p>\n\n\n\n<p>\u22201 = \u22203<\/p>\n\n\n\n<p>\u22202 = \u22204<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"395\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/example-of-vertical-angles-formed-by-two-intersecting-lines.png\" alt=\"Example of vertical angles formed by two intersecting lines\" class=\"wp-image-32963\" title=\"Example of vertical angles formed by two intersecting lines\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/example-of-vertical-angles-formed-by-two-intersecting-lines.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/example-of-vertical-angles-formed-by-two-intersecting-lines-300x191.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>We know that the sum of angles forming a linear pair is 180\u00b0.<\/p>\n\n\n\n<p>\u22201 +\u22202 = 180\u00b0 (linear pair of angles) &#8212;&#8212;&#8212; (1)<\/p>\n\n\n\n<p>\u22201 +\u22204 = 180\u00b0 (linear pair of angles) &#8212;&#8212;&#8212; (2)<\/p>\n\n\n\n<p>From equations (1) and (2), we can see that the RHS is equal.&nbsp;<\/p>\n\n\n\n<p>Equating (1) and (2), we get<\/p>\n\n\n\n<p>\u00a0\u22201 + \u22202 =\u22201 +\u22204<\/p>\n\n\n\n<p>Thus, \u22202 = \u22204<\/p>\n\n\n\n<p>Similarly, we can prove that \u22201 =\u22203<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-are-vertical-angles-adjacent\">Are Vertical Angles Adjacent?<\/h2>\n\n\n\n<p>Vertical angles can never be adjacent. Two adjacent angles share a common vertex and a common arm (or side). Adjacent angles lie next to each other.&nbsp;<\/p>\n\n\n\n<p>On the other hand, the vertical angles lie opposite to each other. They only share a common vertex.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"388\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-and-adjacent-angles.png\" alt=\"Vertical angles and adjacent angles\" class=\"wp-image-32964\" title=\"Vertical angles and adjacent angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-and-adjacent-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-and-adjacent-angles-300x188.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>In the above image, we observe that the angles \u22201 and \u22202 are vertical angles and the angles \u22203 and \u22204 are adjacent angles.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-are-vertical-angles-supplementary\">Are Vertical Angles Supplementary?<\/h2>\n\n\n\n<p>Supplementary angles are the angles which add up to 180\u00b0. Vertical angles are supplementary if and only if the lines intersect each other at a 90\u00b0 angle. In simple words, if the two lines are perpendicular, the vertical angles formed are supplementary.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"406\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-which-are-supplementary.png\" alt=\"Vertical angles which are supplementary\" class=\"wp-image-32965\" title=\"Vertical angles which are supplementary\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-which-are-supplementary.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-which-are-supplementary-300x196.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>We observe in the above case that all the angles are <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-angle\">right angles<\/a> (equal to 90\u00b0).&nbsp;<\/p>\n\n\n\n<p>Thus, the sum of vertical angles will be 90\u00b0 + 90\u00b0 = 180\u00b0.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-are-vertical-angles-complementary\">Are Vertical Angles Complementary?<\/h2>\n\n\n\n<p>We know that vertical angles are always congruent. Complementary angles are the angles that add up to 90\u00b0.&nbsp;<\/p>\n\n\n\n<p>Thus, for two vertical angles to be complementary, each of the angles should measure <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/45-degree-angle\">45\u00b0<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"373\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-that-are-also-complementary.png\" alt=\"Vertical angles that are also complementary\" class=\"wp-image-32966\" title=\"Vertical angles that are also complementary\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-that-are-also-complementary.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-that-are-also-complementary-300x180.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>When we add both the vertical angle pair, we get&nbsp;<\/p>\n\n\n\n<p>45<sup>\u00b0<\/sup>+ 45<sup>\u00b0<\/sup> = 90<sup>\u00b0<\/sup>.\u00a0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-using-vertical-angles-to-find-the-measurement-of-a-missing-angle\">Using Vertical Angles to Find the Measurement of a Missing Angle<\/h2>\n\n\n\n<p>Vertical angles can be very useful when we are given two intersecting lines and we have to find all the missing angles, provided we are given only one angle. Here, we use two important theorems.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A pair of vertical angles are congruent.<\/li>\n\n\n\n<li>Angles in a linear pair are supplementary.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s understand this with an example.<\/p>\n\n\n\n<p><strong>Example: Find the angles x, y, and z.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"398\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/finding-missing-angles-using-vertical-angles.png\" alt=\"Finding missing angles using vertical angles\" class=\"wp-image-32967\" title=\"Finding missing angles using vertical angles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/finding-missing-angles-using-vertical-angles.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/finding-missing-angles-using-vertical-angles-300x193.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>The angle y and the angle measuring 55<sup>\u00b0<\/sup> are vertical angles. Thus, they are congruent.<\/p>\n\n\n\n<p>We can write<\/p>\n\n\n\n<p>y = 55<sup>\u00b0<\/sup><\/p>\n\n\n\n<p>Next, the angle x and y are angles in a linear pair.<\/p>\n\n\n\n<p>Thus, x + y = 180<sup>\u00b0<\/sup><\/p>\n\n\n\n<p>x + 55<sup>\u00b0<\/sup> = 180<sup>\u00b0<\/sup><\/p>\n\n\n\n<p>x = 125<sup>\u00b0<\/sup><\/p>\n\n\n\n<p>Finally, the angles x and z are vertical angles. Thus, x = z = 125<sup>\u00b0<\/sup><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-vertical-angles-around-you\">Vertical Angles Around You<\/h2>\n\n\n\n<p>You can observe vertical angles in everyday objects around you. Take a look!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"590\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-real-life-examples.png\" alt=\"Vertical angles real-life examples\" class=\"wp-image-32968\" title=\"Vertical angles real-life examples\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-real-life-examples.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-real-life-examples-300x285.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-facts-about-vertical-angles\">Facts about Vertical Angles<\/h2>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-0057255f-a6d3-498a-9a8e-4d3f2da817f3\">\n\n\n<p>Vertical angles can never be adjacent; adjacent angles can never be vertical.<br>Vertical angles are always congruent.<\/p>\n\n\n<\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"10-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about vertical angles and their significance in geometry. Vertical angles are formed by intersecting lines and have equal measures, providing valuable insights into various geometric relationships. Now that we have grasped the concept of vertical angles, let&#8217;s take our learning to the next level by putting it into practice. Let&#8217;s solve a few examples and tackle some MCQs to solidify our comprehension.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-solved-examples-on-vertical-angles\">Solved Examples on Vertical Angles<\/h2>\n\n\n\n<p><strong>1. Find the measure of <\/strong>\u2220DCE<strong>. Also, find the other missing angles.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"188\" height=\"202\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-example.png\" alt=\"Vertical angles example\" class=\"wp-image-32969\" title=\"Vertical angles example\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>\u2220DCE and \u2220ACB are vertical angles.<\/p>\n\n\n\n<p>Vertically opposite angles are always equal.&nbsp;<\/p>\n\n\n\n<p>Thus, \u2220DCE  = \u2220ACB  = 65<sup>\u00b0<\/sup><\/p>\n\n\n\n<p>Here, \u2220ACB and \u2220BCE are angles in a linear pair.<\/p>\n\n\n\n<p>\u2220ACB + \u2220BCE  = 180<sup>\u00b0<\/sup><\/p>\n\n\n\n<p>60<sup>\u00b0<\/sup> + \u2220BCE = 180<sup>\u00b0<\/sup><\/p>\n\n\n\n<p>\u2220BCE = 120<sup>\u00b0<\/sup><\/p>\n\n\n\n<p>Also, \u2220BCE and \u2220ACD are vertical angles.<\/p>\n\n\n\n<p>Thus, \u2220BCE = \u2220ACD = 120<sup>\u00b0<\/sup><\/p>\n\n\n\n<p><strong>2. Identify the vertical angles.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"289\" height=\"243\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/three-intersecting-lines-forming-8-angles.png\" alt=\"Three intersecting lines forming 8 angles\" class=\"wp-image-32970\" title=\"Three intersecting lines forming 8 angles\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Vertical angles can be defined as the angles that lie opposite to each other when two lines intersect.&nbsp;<\/p>\n\n\n\n<p>Pairs of vertical angles in the above diagram are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u22201, \u22206<\/strong><\/li>\n\n\n\n<li><strong>\u22202, \u22205<\/strong><\/li>\n\n\n\n<li><strong>\u22203, \u22208<\/strong><\/li>\n\n\n\n<li><strong>\u22204, \u22207<\/strong><\/li>\n<\/ul>\n\n\n\n<p><strong>3. If <\/strong><strong>\u2220<\/strong><strong>p = <\/strong><strong>35<\/strong><strong><sup>\u00b0<\/sup><\/strong><strong>, find <\/strong><strong>m\u2220<\/strong><strong>q.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"216\" height=\"215\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angle-example.png\" alt=\"Vertical angle example\" class=\"wp-image-32971\" title=\"Vertical angle example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angle-example.png 216w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angle-example-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angle-example-120x120.png 120w\" sizes=\"auto, (max-width: 216px) 100vw, 216px\" \/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>From the figure, we can observe that the angle 120\u00b0 and the angle formed by combining p and q are vertically opposite.&nbsp;<\/p>\n\n\n\n<p>Thus, \u2220p + \u2220q = 120\u00b0.\u00a0<\/p>\n\n\n\n<p><strong>35<\/strong><sup>\u00b0<\/sup>+\u2220q = 120\u00b0<\/p>\n\n\n\n<p>\u2220q = 120\u00b0 &#8211; <strong>35<\/strong><sup>\u00b0<\/sup><\/p>\n\n\n\n<p>\u2220q = 85\u00b0<\/p>\n\n\n\n<p><strong>4. Are the angles <\/strong><strong>\u2220<\/strong><strong>AOB and <\/strong><strong>\u2220<\/strong><strong>COD vertical angles? Can we say that<\/strong><strong>\u2220AOB=28\u00b0<\/strong><strong>?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"218\" height=\"123\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/identifying-vertical-angles.png\" alt=\"Identifying vertical angles\" class=\"wp-image-32972\" title=\"Identifying vertical angles\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Vertical angles are formed when two straight lines intersect each other.&nbsp;<\/p>\n\n\n\n<p>In the diagram, you can see that line BO and line OC are two different lines.&nbsp;<\/p>\n\n\n\n<p>The angles \u2220AOB and \u2220COD are not formed by the intersection of two straight lines. Thus, the angles are not vertical.<\/p>\n\n\n\n<p>Hence, \u2220AOB \u2260 28\u00b0.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-practice-problems-on-vertical-angles\">Practice Problems on Vertical Angles<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Vertical Angles - Definition, Theorem, Facts, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Observe the diagram and choose the correct statement.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angles-a-and-b.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">a = 2b<\/div><div class=\"spq_answer_block\" data-value=\"1\">a + b = 90\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">a + b = 180\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">a = b<\/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: a = b<br\/>Angles a and b are vertical angles. Vertically opposite angles are always equal.<br>\r\nSo, a = b<\/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\">Vertical angles are always ________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">complementary<\/div><div class=\"spq_answer_block\" data-value=\"1\">supplementary<\/div><div class=\"spq_answer_block\" data-value=\"2\">congruent<\/div><div class=\"spq_answer_block\" data-value=\"3\">acute<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: congruent<br\/>Vertical angles are always congruent.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the value of x?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angle-example-1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">38\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">48\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">35\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">58\u00b0<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 35\u00b0<br\/>(5x \u2013 70)\u00b0 = 105\u00b0 \t\t\u2026(vertically opposite angles)<br>\r\n5x = 175\u00b0<br>\r\nx = 35\u00b0<\/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\">Vertical angles formed are supplementary when the two lines are ____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">parallel<\/div><div class=\"spq_answer_block\" data-value=\"1\">perpendicular<\/div><div class=\"spq_answer_block\" data-value=\"2\">equidistant<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/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: perpendicular<br\/>If the two lines are perpendicular, the vertical angles formed are supplementary.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">If two vertical angles are complementary, then each angle measures<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">90\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">40\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">45\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">60\u00b0<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 45\u00b0<br\/>If two vertical angles are complementary, then each angle measures 45\u00b0.<br>\r\n45\u00b0 + 45\u00b0 = 90\u00b0<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Vertical Angles - 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\"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of x?\",\n                    \"text\": \"What is the value of x? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/vertical-angle-example-1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"(5x \u2013 70)\u00b0 = 105\u00b0 \t\t\u2026(vertically opposite angles)<br>\r\n5x = 175\u00b0<br>\r\nx = 35\u00b0\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"38\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"(5x \u2013 70)\u00b0 = 105\u00b0 \t\t\u2026(vertically opposite angles)<br>\r\n5x = 175\u00b0<br>\r\nx = 35\u00b0\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"48\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"(5x \u2013 70)\u00b0 = 105\u00b0 \t\t\u2026(vertically opposite angles)<br>\r\n5x = 175\u00b0<br>\r\nx = 35\u00b0\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"58\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"(5x \u2013 70)\u00b0 = 105\u00b0 \t\t\u2026(vertically opposite angles)<br>\r\n5x = 175\u00b0<br>\r\nx = 35\u00b0\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"35\u00b0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"(5x \u2013 70)\u00b0 = 105\u00b0 \t\t\u2026(vertically opposite angles)<br>\r\n5x = 175\u00b0<br>\r\nx = 35\u00b0\"\n                 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\"encodingFormat\": \"text\/html\",\n                                \"text\": \"40\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two vertical angles are complementary, then each angle measures 45\u00b0.<br>\r\n45\u00b0 + 45\u00b0 = 90\u00b0\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"60\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If two vertical angles are complementary, then each angle measures 45\u00b0.<br>\r\n45\u00b0 + 45\u00b0 = 90\u00b0\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"45\u00b0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If two vertical angles are complementary, then each angle measures 45\u00b0.<br>\r\n45\u00b0 + 45\u00b0 = 90\u00b0\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If two vertical angles are complementary, then each angle measures 45\u00b0.<br>\r\n45\u00b0 + 45\u00b0 = 90\u00b0\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-frequently-asked-questions-on-vertical-angles\">Frequently Asked Questions on Vertical Angles<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-f75ff920-0be3-4ccf-af01-23fe1f341a9d\" 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-f75ff920-0be3-4ccf-af01-23fe1f341a9d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f75ff920-0be3-4ccf-af01-23fe1f341a9d\"><strong>What does it mean when vertical angles measure 90\u00b0?<\/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-f75ff920-0be3-4ccf-af01-23fe1f341a9d\">\n\n<p>If vertical angles measure 90\u00b0, it means that the lines forming them are perpendicular.<\/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-f75ff920-0be3-4ccf-af01-23fe1f341a9d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f75ff920-0be3-4ccf-af01-23fe1f341a9d\"><strong>Are vertical angles always congruent?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-f75ff920-0be3-4ccf-af01-23fe1f341a9d\">\n\n<p>Yes, vertical angles are always congruent.<\/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-f75ff920-0be3-4ccf-af01-23fe1f341a9d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f75ff920-0be3-4ccf-af01-23fe1f341a9d\"><strong>What is meant by interior and exterior angles?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-f75ff920-0be3-4ccf-af01-23fe1f341a9d\">\n\n<p>The angles that are formed inside of a shape by the sides are known as the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles\">interior angles<\/a>, whereas the angles formed on the outside of the shape are known as the\u00a0exterior 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-3-f75ff920-0be3-4ccf-af01-23fe1f341a9d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f75ff920-0be3-4ccf-af01-23fe1f341a9d\"><strong>Why are vertical angles always congruent?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-f75ff920-0be3-4ccf-af01-23fe1f341a9d\">\n\n<p>Vertical angles are always congruent due to their position; they are formed by the intersection of two lines, creating opposite angles with equal measures. This geometric property is a result of the angles sharing a common vertex and being on opposite sides of the intersecting lines, leading to their equal measures.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Vertical Angles? Whenever two lines cross or intersect each other, four angles are formed. Out of these, the angles opposite to each other are called vertical angles or vertically opposite angles. Vertical angles are always congruent.&nbsp; Here, the pairs of vertical angles are Observe that the two angles opposite to each other are &#8230; <a title=\"Vertical Angles &#8211; Definition, Theorem, Facts, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/vertical-angles\" aria-label=\"More on Vertical Angles &#8211; Definition, Theorem, Facts, 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-32896","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\/32896","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=32896"}],"version-history":[{"count":7,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32896\/revisions"}],"predecessor-version":[{"id":32982,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32896\/revisions\/32982"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=32896"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=32896"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=32896"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}