{"id":17829,"date":"2023-01-05T14:18:11","date_gmt":"2023-01-05T14:18:11","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=17829"},"modified":"2024-01-01T16:25:58","modified_gmt":"2024-01-01T16:25:58","slug":"central-angle","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/central-angle","title":{"rendered":"Central Angle"},"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-98999775-c963-4bf9-bbb8-f1378ff191ae\" 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\/geometry\/central-angle#0-introduction-to-the-central-angle>Introduction to the Central Angle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/central-angle#4-central-angle-theorem>Central Angle Theorem<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/central-angle#5-how-to-find-the-central-angle>How to Find the Central Angle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/central-angle#7-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/central-angle#8-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/central-angle#9-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-introduction-to-the-central-angle\">Introduction to the Central Angle<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A central angle is formed when two circle radii form a vertex at the central point of a circle. These arms of the circle may originate at two different points along the arc of such a circle. As a result of their intersection, the two radii form a central angle that helps to segregate a circle into different sectors.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider the example of a pizza. Have you noticed how slicing it into different pieces makes it possible to divide one whole pizza into smaller slices? A protractor is another central angle example.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"335\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/central-angle-in-a-protractor.png\" alt=\"Central angle in a protractor\" class=\"wp-image-37130\" title=\"Central angle in a protractor\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/central-angle-in-a-protractor.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/central-angle-in-a-protractor-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-the-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_add_angles_pt.png\" alt=\"Add the Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add the Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-in-multiples-of-10-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_1_pt.png\" alt=\"Draw Angles in Multiples of 10 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles in Multiples of 10 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-nearest-5-and-1-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_2_pt.png\" alt=\"Draw Angles Nearest 5 and 1 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles Nearest 5 and 1 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-using-a-protractor\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_protractor_pt.png\" alt=\"Draw Angles Using a Protractor Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles Using a Protractor Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-right-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_right_angle_1_pt.png\" alt=\"Find Right Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Right Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-perimeter-of-the-squared-and-the-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_peri_rectangle_2_pt.png\" alt=\"Find the Perimeter of the Squared and the Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Perimeter of the Squared and the Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-angles-by-their-types\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_types_of_angle_pt.png\" alt=\"Identify Angles by their Types Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Angles by their Types Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-what-is-a-central-angle-in-geometry\">What Is a Central Angle in Geometry?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A central angle is formed at the center of a circle due to the intersection of any two radii within the circle. As stated, a central angle in geometry is one whose vertex forms at the center of the circle, with two radii forming its arms that intersect the circle at two different points.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Joining these two points will yield an arc on the circle. So, we can also say that a central angle is the angle where an arc subtends at the center of a circle. There is no special central angle symbol.<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/count-sides-and-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/count-sides-and-angles.jpeg\" alt=\"Count Sides and Angles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rectangles-and-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/separate-out-the-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/separate-out-the-triangles.jpeg\" alt=\"Separate Out the Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-center-angle-of-a-circle-characteristics-uses-importance\">Center Angle of a Circle: Characteristics, Uses, Importance<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When a central angle forms at the center of a circle, we can observe certain properties of the figure, such as:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The measure of the central angle is congruent to the measurement of the arc that it intercepts.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">All congruent central angles form congruent arcs in a circle, and the reverse is also true.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">All congruent central angles form congruent chords in a circle, and the reverse is also true.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The central angle measures twice the inscribed angle, subtended by the same arc.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">If we were to take measurements of all the central angles of a circle without a common point, the total would come out to $360^\\circ$.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Knowledge of the central angle is essential to solve problems relating to angles in a circle. The central angle is essential to calculate the arc length and the sector\u2019s area. With the measure of the central angle in hand, we can easily calculate the other measures related to the angle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-central-angle-formula\">Central Angle Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The formula for central angle is calculated using the measure of arc and the inscribed angle of the circle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The central angle is congruent to the intercepted arc. Thus,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Central angle $=$ Intercepted arc<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The central angle is twice the inscribed angle subtended by the same arc. Thus,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Central angle $= 2$ (inscribed angle)<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Central angle $= \\frac{Arc Length}{Radius}$<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Central angle $= \\frac{2(area of sector)}{(Radius)^2}$&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can also denote the central angle formula as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Central Angle $= s \\times \\frac{360}{2 \\pi r}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here \u201c<em>s<\/em>\u201d is the length of the arc, and \u201c<em>r<\/em>\u201d is the radius of the circle<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-central-angle-theorem\">Central Angle Theorem<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/central-angle-theorem.png\" alt=\"Central angle theorem\" class=\"wp-image-37131\" title=\"Central angle theorem\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/central-angle-theorem.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/central-angle-theorem-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">According to the theorem of central angle measure<em>, <\/em>the angle subtended by an arc at the center of a circle is double the angle subtended by it at any other point on the circle\u2019s circumference.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-how-to-find-the-central-angle\">How to Find the Central Angle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To calculate the central angle, we must find out the length of the arc and the radius. The below-mentioned steps elucidate how to find the center of the angle:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Locate the endpoints of the arc and the central point of the circle.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Connect the endpoints of the arc with the center of the circle. Also, take a measure of the lengths of the arc and the radius.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Use the formula <strong>Central Angle <\/strong>$= \\frac{Length of the Arc}{Radius}$&nbsp; to obtain the measure of the central angle.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-how-to-find-the-central-angle-and-intercepted-arc\">How to Find the Central Angle and Intercepted Arc?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s discuss the Intercepted Arc formula and examples. We can find the central angle of a circle using the intercepted arc formula, which states the following:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Central angle $=$ Measure of the intercepted arc<\/li>\n\n\n\n<li class=\"eplus-wrapper\">2 (inscribed angle) $=$ Central angle<\/li>\n\n\n\n<li class=\"eplus-wrapper\">2 (inscribed angle) $=$ Intercepted arc<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Inscribed angle $=$ Half the sum of the intercepted arcs<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Supposing Mr. A divides a circle into four equal parts using two diameters, how can we measure the central or inscribed angle of each section of such a circle?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution: <\/strong>We know that the complete angle in a circle $= 360$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since the circle is divided into 4 equal parts, the angle of each section $= \\frac{360}{4}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The central angle of each quadrant will be $90^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. If the arc of a circle has a length of 8 cm and the central angle measures <\/strong>$120^\\circ$<strong>, what will be the radius of such an arc? (Use <\/strong>$\\pi = 3.14$<strong>)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the central angle $= 120^\\circ$, and the arc length is 8 inches.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Using the formula, Central Angle $= s \\times \\frac{360}{2 \\pi r}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">where, \u201c<em>s<\/em>\u201d is the length of the arc, and \u201c<em>r<\/em>\u201d is the radius of the circle<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$120^\\circ = 8 \\times \\frac{360}{2 \\pi r}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$r = \\frac{8 \\times 360}{2 \\pi \\times120}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$r = \\frac{2880}{753.6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$r = 3.821$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The radius of the arc is 3.821 cm.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. If an arc length is 11 inches and the radius of a circle is 7 inches, what will be the angle of the arc? (Use <\/strong>$\\pi =227$<strong>)<\/strong><\/p>\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 that length of the arc $= 11$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The radius of the arc $= 7$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Central Angle $= s \\times \\frac{360}{2 \\pi r}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">where, \u201c<em>s<\/em>\u201d is the length of the arc, and \u201c<em>r<\/em>\u201d is the radius of the circle<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Central Angle $= \\frac{11 \\times 360}{2} \\times \\frac{22}{7} \\times 7 = 90^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The angle will be $90^\\circ$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. In the circle below, find out the value of \u201c<\/strong><strong><em>a<\/em><\/strong><strong>.\u201d<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"281\" height=\"196\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/central-angle-degree.png\" alt=\"Central angle 60\u00b0\" class=\"wp-image-37133\" title=\"Central angle 60\u00b0\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that the central angle $=$ intercepted arc<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$4a + 8 = 60$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Solving the equation, we can get the value of <em>a<\/em>.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The value of <em>a<\/em> will be 13.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. In the circle below, find out the measure of <\/strong>$\\angle \\text{AOB}$<strong>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"277\" height=\"290\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/central-angle-theorem-example.png\" alt=\"Central angle theorem example\" class=\"wp-image-37134\" title=\"Central angle theorem example\"\/><\/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\">We know that $\\angle \\text{AOB}$ is a central angle, and $\\angle \\text{ACB}$ is the inscribed angle.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Also, the central angle is twice the inscribed angle if they are subtended on the same arc.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $\\angle {AOB} = 2 \\angle \\text{ACB}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle \\text{AOB} = 2(64^\\circ)$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\angle \\text{AOB} = 128^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The measure of $\\angle \\text{AOB is} 128^\\circ$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Central Angle<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">For which of the following figures can we calculate a central angle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Square<\/div><div class=\"spq_answer_block\" data-value=\"1\">Circle<\/div><div class=\"spq_answer_block\" data-value=\"2\">Triangle<\/div><div class=\"spq_answer_block\" data-value=\"3\">Rectangle<\/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: Circle<br\/>A central angle is formed by the intersection of two radii, which is only a feature of a circle.<\/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\">If the clock is currently showing the time as 9:00 hours, what is the central angle between the hands of the clock?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$180^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$120^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$30^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$90^\\circ$<\/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\/>At 9:00 hours, the two hands of the clock divide the entire clock into four equal segments, which makes the central angle between them $90^\\circ$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If the arc of a circle has a length of 10 cm and the central angle measures $120^\\circ$, what will be the radius of such an arc? (Use $\\pi = 3.14$)<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4.77 cm<\/div><div class=\"spq_answer_block\" data-value=\"1\">5.48 cm<\/div><div class=\"spq_answer_block\" data-value=\"2\">54.2 cm<\/div><div class=\"spq_answer_block\" data-value=\"3\">25.4 cm<\/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: 4.77 cm<br\/>We know that<br>\r\nCentral Angle$= s \\times \\frac{360}{2 \\pi r}$<br>\r\nwhere, \u201cs\u201d is the length of the arc, and \u201cr\u201d is the radius of the circle<br>\r\n$120^\\circ = 10 \\times \\frac{360}{2 \\pi r}$<br>\r\nr $=  \\frac{10 \\times 360}{753.6}$<br>\r\nr $= 4.77$ cm<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If the central angle is $70^\\circ$ and the intercepted arc is denoted by the equation $6a + 10$, what will be the value of \u201ca\u201d?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">10<\/div><div class=\"spq_answer_block\" data-value=\"1\">20<\/div><div class=\"spq_answer_block\" data-value=\"2\">30<\/div><div class=\"spq_answer_block\" data-value=\"3\">10<\/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: 10<br\/>We know that the central angle $=$ intercepted arc<br>\r\n$6a + 10 = 70$<br>\r\nSolving the equation, we can get the value of a.<\/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\": \"Central Angle\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Central Angle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"For which of the following figures can we calculate a central angle?\",\n                    \"text\": \"For which of the following figures can we calculate a central angle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A central angle is formed by the intersection of two radii, which is only a feature of a circle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Square\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A central angle is formed by the intersection of two radii, which is only a feature of a circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Triangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A central angle is formed by the intersection of two radii, which is only a feature of a circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Rectangle\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A central angle is formed by the intersection of two radii, which is only a feature of a circle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Circle\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A central angle is formed by the intersection of two radii, which is only a feature of a circle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A central angle is formed by the intersection of two radii, which is only a feature of a circle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the clock is currently showing the time as 9:00 hours, what is the central angle between the hands of the clock?\",\n                    \"text\": \"If the clock is currently showing the time as 9:00 hours, what is the central angle between the hands of the clock?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"At 9:00 hours, the two hands of the clock divide the entire clock into four equal segments, which makes the central angle between them $$90^\\\\circ$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$180^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"At 9:00 hours, the two hands of the clock divide the entire clock into four equal segments, which makes the central angle between them $$90^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$120^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"At 9:00 hours, the two hands of the clock divide the entire clock into four equal segments, which makes the central angle between them $$90^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$30^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"At 9:00 hours, the two hands of the clock divide the entire clock into four equal segments, which makes the central angle between them $$90^\\\\circ$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$90^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"At 9:00 hours, the two hands of the clock divide the entire clock into four equal segments, which makes the central angle between them $$90^\\\\circ$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"At 9:00 hours, the two hands of the clock divide the entire clock into four equal segments, which makes the central angle between them $$90^\\\\circ$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the arc of a circle has a length of 10 cm and the central angle measures $$120^\\\\circ$$, what will be the radius of such an arc? (Use $$\\\\pi = 3.14$$)\",\n                    \"text\": \"If the arc of a circle has a length of 10 cm and the central angle measures $$120^\\\\circ$$, what will be the radius of such an arc? (Use $$\\\\pi = 3.14$$)\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that<br>\r\nCentral Angle$$= s \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nwhere, \u201cs\u201d is the length of the arc, and \u201cr\u201d is the radius of the circle<br>\r\n$$120^\\\\circ = 10 \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nr $$=  \\\\frac{10 \\\\times 360}{753.6}$$<br>\r\nr $$= 4.77$$ cm\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5.48 cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that<br>\r\nCentral Angle$$= s \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nwhere, \u201cs\u201d is the length of the arc, and \u201cr\u201d is the radius of the circle<br>\r\n$$120^\\\\circ = 10 \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nr $$=  \\\\frac{10 \\\\times 360}{753.6}$$<br>\r\nr $$= 4.77$$ cm\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"54.2 cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that<br>\r\nCentral Angle$$= s \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nwhere, \u201cs\u201d is the length of the arc, and \u201cr\u201d is the radius of the circle<br>\r\n$$120^\\\\circ = 10 \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nr $$=  \\\\frac{10 \\\\times 360}{753.6}$$<br>\r\nr $$= 4.77$$ cm\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"25.4 cm\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that<br>\r\nCentral Angle$$= s \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nwhere, \u201cs\u201d is the length of the arc, and \u201cr\u201d is the radius of the circle<br>\r\n$$120^\\\\circ = 10 \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nr $$=  \\\\frac{10 \\\\times 360}{753.6}$$<br>\r\nr $$= 4.77$$ cm\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"4.77 cm\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that<br>\r\nCentral Angle$$= s \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nwhere, \u201cs\u201d is the length of the arc, and \u201cr\u201d is the radius of the circle<br>\r\n$$120^\\\\circ = 10 \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nr $$=  \\\\frac{10 \\\\times 360}{753.6}$$<br>\r\nr $$= 4.77$$ cm\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that<br>\r\nCentral Angle$$= s \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nwhere, \u201cs\u201d is the length of the arc, and \u201cr\u201d is the radius of the circle<br>\r\n$$120^\\\\circ = 10 \\\\times \\\\frac{360}{2 \\\\pi r}$$<br>\r\nr $$=  \\\\frac{10 \\\\times 360}{753.6}$$<br>\r\nr $$= 4.77$$ cm\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the central angle is $$70^\\\\circ$$ and the intercepted arc is denoted by the equation $$6a + 10$$, what will be the value of \u201ca\u201d?\",\n                    \"text\": \"If the central angle is $$70^\\\\circ$$ and the intercepted arc is denoted by the equation $$6a + 10$$, what will be the value of \u201ca\u201d?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We know that the central angle $$=$$ intercepted arc<br>\r\n$$6a + 10 = 70$$<br>\r\nSolving the equation, we can get the value of a.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the central angle $$=$$ intercepted arc<br>\r\n$$6a + 10 = 70$$<br>\r\nSolving the equation, we can get the value of a.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the central angle $$=$$ intercepted arc<br>\r\n$$6a + 10 = 70$$<br>\r\nSolving the equation, we can get the value of a.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We know that the central angle $$=$$ intercepted arc<br>\r\n$$6a + 10 = 70$$<br>\r\nSolving the equation, we can get the value of a.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"10\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We know that the central angle $$=$$ intercepted arc<br>\r\n$$6a + 10 = 70$$<br>\r\nSolving the equation, we can get the value of a.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We know that the central angle $$=$$ intercepted arc<br>\r\n$$6a + 10 = 70$$<br>\r\nSolving the equation, we can get the value of a.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-58440758-4d06-4b04-98e6-c83414b3e3ce\" 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-0-58440758-4d06-4b04-98e6-c83414b3e3ce\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-58440758-4d06-4b04-98e6-c83414b3e3ce\"><strong>What does the degree of the central angle of a circle mean?<\/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-0-58440758-4d06-4b04-98e6-c83414b3e3ce\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The degree of a central angle is the angle at the center of a circle made by an arc.<\/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-1-58440758-4d06-4b04-98e6-c83414b3e3ce\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-58440758-4d06-4b04-98e6-c83414b3e3ce\"><strong>What is the measure of a central angle made by a semicircle?<\/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-1-58440758-4d06-4b04-98e6-c83414b3e3ce\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A semicircle makes a central angle of $180^\\circ$.<\/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-2-58440758-4d06-4b04-98e6-c83414b3e3ce\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-58440758-4d06-4b04-98e6-c83414b3e3ce\"><strong>What is an inscribed angle?<\/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-2-58440758-4d06-4b04-98e6-c83414b3e3ce\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An inscribed angle is an angle subtended by an arc at any point on a circle.<\/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-3-58440758-4d06-4b04-98e6-c83414b3e3ce\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-58440758-4d06-4b04-98e6-c83414b3e3ce\"><strong>How are central angles and inscribed angles different?<\/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-3-58440758-4d06-4b04-98e6-c83414b3e3ce\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A central angle is an angle subtended by an arc at the center of a circle, whereas an inscribed angle is an angle subtended by an arc at any point on the circumference of the circle.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Introduction to the Central Angle A central angle is formed when two circle radii form a vertex at the central point of a circle. These arms of the circle may originate at two different points along the arc of such a circle. As a result of their intersection, the two radii form a central angle &#8230; <a title=\"Central Angle\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/central-angle\" aria-label=\"More on Central Angle\">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-17829","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\/17829","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=17829"}],"version-history":[{"count":19,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/17829\/revisions"}],"predecessor-version":[{"id":37135,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/17829\/revisions\/37135"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=17829"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=17829"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=17829"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}