{"id":225373,"date":"2025-06-04T07:38:17","date_gmt":"2025-06-04T07:38:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225373"},"modified":"2025-06-04T07:38:20","modified_gmt":"2025-06-04T07:38:20","slug":"question-5-of-10-2-points-what-is-the-measure-of","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/question-5-of-10-2-points-what-is-the-measure-of\/","title":{"rendered":"Question 5 of 10 2 Points What is the measure of"},"content":{"rendered":"\n<p>Question 5 of 10 2 Points What is the measure of<br>? A. 55\u00b0 B. 60\u00b0 C. 30\u00b0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-106.png\" alt=\"\" class=\"wp-image-225374\"\/><\/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>To find the measure of angle \u2220RIA, we need to analyze the diagram provided.<\/p>\n\n\n\n<p>From the image:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angle \u2220FIK is given as <strong>30\u00b0<\/strong>.<\/li>\n\n\n\n<li>Angle \u2220KIN is given as <strong>95\u00b0<\/strong>.<\/li>\n\n\n\n<li>All angles are centered at point <strong>I<\/strong>, and the rays are arranged around point I forming adjacent angles.<\/li>\n\n\n\n<li>To find \u2220RIA, we need to consider the full straight angle around point I, which totals <strong>360\u00b0<\/strong>.<\/li>\n\n\n\n<li>The relevant angles that add up to form the full circle around point I are arranged in this order: <strong>F \u2192 L \u2192 K \u2192 N \u2192 A \u2192 R<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s calculate angle \u2220RIA step-by-step:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u2220FIK = 30\u00b0<\/li>\n\n\n\n<li>\u2220KIN = 95\u00b0<br>Therefore, \u2220FIK + \u2220KIN = 30\u00b0 + 95\u00b0 = <strong>125\u00b0<\/strong><\/li>\n<\/ol>\n\n\n\n<p>Now, \u2220RIA is the angle between ray <strong>IR<\/strong> and <strong>IA<\/strong>. From the diagram, we see that R, I, A are separated from the angles already measured (\u2220FIK and \u2220KIN), meaning the remaining angles around point I total:<\/p>\n\n\n\n<p>360\u00b0 (full circle) \u2212 125\u00b0 = <strong>235\u00b0<\/strong><\/p>\n\n\n\n<p>This 235\u00b0 includes angle \u2220RIA. Looking at the diagram, the angle \u2220RIA spans from ray IR to ray IA, passing through the remaining part of the circle.<\/p>\n\n\n\n<p>Let\u2019s check the specific location:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>IR to IA covers just <strong>part<\/strong> of the remaining 235\u00b0, not all of it. In fact, R to A is just one segment out of the three remaining between K, N, A, and R.<\/li>\n<\/ul>\n\n\n\n<p>From the diagram, \u2220RIA is adjacent to the 95\u00b0 angle (\u2220KIN), and lies between ray IR and ray IA. If we look carefully, R to A is one segment following the 95\u00b0, and the full circle continues from there.<\/p>\n\n\n\n<p>To get the measure of \u2220RIA:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The total around point I is 360\u00b0<\/li>\n\n\n\n<li>From K to N is 95\u00b0<\/li>\n\n\n\n<li>From F to K is 30\u00b0<\/li>\n\n\n\n<li>From R to A (\u2220RIA) looks to be the remaining adjacent angle between the 95\u00b0 and the rest.<\/li>\n<\/ul>\n\n\n\n<p>So if we go clockwise from IR to IA (covering just that section), we can observe:<\/p>\n\n\n\n<p>\u2220RIA = 180\u00b0 \u2212 (95\u00b0 + 30\u00b0) = <strong>55\u00b0<\/strong><\/p>\n\n\n\n<p>Thus, the correct answer is:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 A. 55\u00b0<\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>In geometry, when angles are formed around a central point by intersecting lines or rays, they combine to form a full angle of <strong>360\u00b0<\/strong>. In this diagram, all the rays meet at point <strong>I<\/strong>, forming several adjacent angles.<\/p>\n\n\n\n<p>We are asked to find the measure of angle <strong>\u2220RIA<\/strong>, the angle between ray <strong>IR<\/strong> and ray <strong>IA<\/strong>. From the image, we can see other angles marked: \u2220FIK = 30\u00b0 and \u2220KIN = 95\u00b0. These two angles together form a partial rotation around point I, totaling <strong>125\u00b0<\/strong>.<\/p>\n\n\n\n<p>Since a full circle around a point measures 360\u00b0, the remaining angles (not including \u2220FIK and \u2220KIN) must total <strong>360\u00b0 \u2212 125\u00b0 = 235\u00b0<\/strong>. However, angle \u2220RIA is just one part of this remaining section.<\/p>\n\n\n\n<p>Looking closely at the image, the rays IR and IA are adjacent, with IA coming right after IR in the clockwise direction. That means \u2220RIA does not include the full remaining 235\u00b0, but only a portion of it.<\/p>\n\n\n\n<p>To find this portion, we observe how the angles are positioned. Since IR and IA are separated by one of the remaining sections, and since adjacent angles form straight lines, we can subtract the known angles from 180\u00b0. Specifically, \u2220RIA and the 125\u00b0 (which includes \u2220FIK and \u2220KIN) together form a straight angle (180\u00b0).<\/p>\n\n\n\n<p>So, \u2220RIA = 180\u00b0 \u2212 125\u00b0 = <strong>55\u00b0<\/strong>.<\/p>\n\n\n\n<p>Hence, the correct answer is:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 A. 55\u00b0<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-306.jpeg\" alt=\"\" class=\"wp-image-225375\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Question 5 of 10 2 Points What is the measure of? A. 55\u00b0 B. 60\u00b0 C. 30\u00b0 The Correct Answer and Explanation is: To find the measure of angle \u2220RIA, we need to analyze the diagram provided. From the image: Let\u2019s calculate angle \u2220RIA step-by-step: Now, \u2220RIA is the angle between ray IR and IA. [&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-225373","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225373","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=225373"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225373\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225373"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225373"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}