Circle g is inscribed with triangle e f d. point c is on the circle between points e and f. angle e is 79 degrees. the measure of arc e d is 104 degrees. what is the measure of arc ecf in circle g? 52\u00c2\u00b0 98\u00c2\u00b0 158\u00c2\u00b0 177\u00c2\u00b0<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve for the measure of arc ( \\text{ECF} ) in circle ( G ), we need to understand the relationship between the given angle and the corresponding arcs in the circle.<\/p>\n\n\n\n When an angle is inscribed in a circle, the measure of the angle is half the measure of the intercepted arc. This is known as the inscribed angle theorem<\/strong>. In this problem, the angle ( \\angle E ) is inscribed and has a measure of 79\u00b0. This angle intercepts the arc between points ( E ) and ( F ) on the circle.<\/p>\n\n\n\n The measure of arc ( EF ) can be determined by the relationship: We are told that point ( C ) is on the circle between points ( E ) and ( F ), meaning arc ( EC ) is part of arc ( EF ). Therefore, the measure of arc ( EC ) is a portion of arc ( EF ).<\/p>\n\n\n\n We are also given the measure of arc ( ED ), which is 104\u00b0. The total measure of the circle is 360\u00b0, and we can find the measure of arc ( EF ) + arc ( ED ) by subtracting from 360\u00b0: Thus, we get the measure of arc ( ECF )<\/p>\n","protected":false},"excerpt":{"rendered":" Circle g is inscribed with triangle e f d. point c is on the circle between points e and f. angle e is 79 degrees. the measure of arc e d is 104 degrees. what is the measure of arc ecf in circle g? 52\u00c2\u00b0 98\u00c2\u00b0 158\u00c2\u00b0 177\u00c2\u00b0 The Correct Answer and Explanation is: To […]<\/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-166638","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166638","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=166638"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166638\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=166638"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=166638"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=166638"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understand the relationship between angles and arcs<\/h3>\n\n\n\n
Step 2: Use the inscribed angle theorem<\/h3>\n\n\n\n
[
\\text{Arc } EF = 2 \\times \\angle E = 2 \\times 79\u00b0 = 158\u00b0
]
Thus, the measure of arc ( EF ) is 158\u00b0.<\/p>\n\n\n\nStep 3: Calculate the measure of arc ( EC )<\/h3>\n\n\n\n
[
\\text{Arc } EF + \\text{Arc } ED = 360\u00b0 – \\text{Arc } ECF.
]<\/p>\n\n\n\n