{"id":253074,"date":"2025-07-11T18:20:49","date_gmt":"2025-07-11T18:20:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=253074"},"modified":"2025-07-11T18:20:56","modified_gmt":"2025-07-11T18:20:56","slug":"name-the-major-arc-and-find-its-measure","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/name-the-major-arc-and-find-its-measure\/","title":{"rendered":"Name the major arc and find its measure"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">3 0.25 points Name the major arc and find its measure. B A 75 ^ C D Arc type your answer... Previous The measure of the arc is type your answer... degrees<\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-413.png\" alt=\"\" class=\"wp-image-253075\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Arc:<\/strong>&nbsp;ADB<\/p>\n\n\n\n<p><strong>The measure of the arc is:<\/strong>&nbsp;285 degrees<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>This problem requires us to identify the major arc in the given circle and calculate its measure.<\/p>\n\n\n\n<p>First, it is important to understand the definitions of different types of arcs in a circle. A minor arc is the shorter path along the circle between two points, and its measure is always less than 180 degrees. A major arc is the longer path between the same two points, and its measure is always greater than 180 degrees. A full circle comprises 360 degrees.<\/p>\n\n\n\n<p>In the provided diagram, we have a circle with its center at point C. The points A, B, and D are located on the circumference of the circle. We are given the measure of the central angle \u2220ACB, which is 75 degrees. The measure of a minor arc is equal to the measure of its corresponding central angle. In this case, the central angle \u2220ACB subtends the minor arc that connects points A and B. Therefore, the measure of the minor arc AB is 75 degrees.<\/p>\n\n\n\n<p>The question asks for the name and measure of the major arc. The major arc is the longer path from point A to point B that does not pass directly between them. To avoid confusion with the minor arc, a major arc is typically named using three letters: the two endpoints and another point that lies on the arc. In this diagram, the point D is on the longer path between A and B, so the major arc is named arc ADB.<\/p>\n\n\n\n<p>To find the measure of the major arc ADB, we subtract the measure of the corresponding minor arc AB from the total degrees in a full circle.<\/p>\n\n\n\n<p>The calculation is performed as follows:<\/p>\n\n\n\n<p>Measure of major arc ADB = (Total degrees in a circle) \u2013 (Measure of minor arc AB)<br>Measure of major arc ADB = 360\u00b0 \u2013 75\u00b0<br>Measure of major arc ADB = 285\u00b0<\/p>\n\n\n\n<p>Thus, the major arc is correctly named arc ADB, and its measure is 285 degrees.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-332.jpeg\" alt=\"\" class=\"wp-image-253076\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>3 0.25 points Name the major arc and find its measure. B A 75 ^ C D Arc type your answer&#8230; Previous The measure of the arc is type your answer&#8230; degrees The Correct Answer and Explanation is: Arc:&nbsp;ADB The measure of the arc is:&nbsp;285 degrees Explanation This problem requires us to identify the major [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-253074","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253074","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=253074"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253074\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253074"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253074"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253074"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}