{"id":246800,"date":"2025-07-07T12:54:04","date_gmt":"2025-07-07T12:54:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246800"},"modified":"2025-07-07T12:54:06","modified_gmt":"2025-07-07T12:54:06","slug":"triangle-abc-has-the-angle-measures-shown","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/07\/triangle-abc-has-the-angle-measures-shown\/","title":{"rendered":"Triangle ABC has the angle measures shown."},"content":{"rendered":"\n<p>Triangle ABC has the angle measures shown. Measure of angle A = (2 x) degrees. Measure of angle B = (3 x) degrees. Measure of angle C = (4 x) degrees. Which statement is true about the angles? Measure of angle A = 20 degrees Measure of angle B = 60 degrees Angle A and Angle B are complementary Measure of angle A + measure of angle C = 100 degrees<\/p>\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>Let&#8217;s break this down step by step.<\/p>\n\n\n\n<p>We are given that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Measure of angle A = 2x<\/li>\n\n\n\n<li>Measure of angle B = 3x<\/li>\n\n\n\n<li>Measure of angle C = 4x<\/li>\n<\/ul>\n\n\n\n<p>In any triangle, the sum of the angles must always be 180 degrees. Therefore, we can set up the following equation:Angle&nbsp;A+Angle&nbsp;B+Angle&nbsp;C=180\u2218\\text{Angle A} + \\text{Angle B} + \\text{Angle C} = 180^\\circAngle&nbsp;A+Angle&nbsp;B+Angle&nbsp;C=180\u2218<\/p>\n\n\n\n<p>Substituting the expressions for the angles in terms of xxx:2x+3x+4x=1802x + 3x + 4x = 1802x+3x+4x=180<\/p>\n\n\n\n<p>Simplifying the left side:9x=1809x = 1809x=180<\/p>\n\n\n\n<p>Now, solving for xxx:x=1809=20x = \\frac{180}{9} = 20x=9180\u200b=20<\/p>\n\n\n\n<p>Now that we know x=20x = 20x=20, we can find the measures of the individual angles:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Measure of angle A = 2x=2(20)=40\u22182x = 2(20) = 40^\\circ2x=2(20)=40\u2218<\/li>\n\n\n\n<li>Measure of angle B = 3x=3(20)=60\u22183x = 3(20) = 60^\\circ3x=3(20)=60\u2218<\/li>\n\n\n\n<li>Measure of angle C = 4x=4(20)=80\u22184x = 4(20) = 80^\\circ4x=4(20)=80\u2218<\/li>\n<\/ul>\n\n\n\n<p>Now, let&#8217;s go through the given options:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Measure of angle A = 20 degrees<\/strong>: This is incorrect because we found that angle A is 40 degrees, not 20 degrees.<\/li>\n\n\n\n<li><strong>Measure of angle B = 60 degrees<\/strong>: This is correct since we calculated that angle B is 60 degrees.<\/li>\n\n\n\n<li><strong>Angle A and Angle B are complementary<\/strong>: Complementary angles add up to 90 degrees. But angle A is 40 degrees, and angle B is 60 degrees. Together, they add up to 100 degrees, not 90, so this is false.<\/li>\n\n\n\n<li><strong>Measure of angle A + measure of angle C = 100 degrees<\/strong>: This is correct because angle A is 40 degrees, and angle C is 80 degrees, so 40+80=10040 + 80 = 10040+80=100 degrees.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The correct statements are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Measure of angle B = 60 degrees<\/li>\n\n\n\n<li>Measure of angle A + measure of angle C = 100 degrees<\/li>\n<\/ul>\n\n\n\n<p>These two statements are true.<\/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-banner5-944.jpeg\" alt=\"\" class=\"wp-image-246801\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Triangle ABC has the angle measures shown. Measure of angle A = (2 x) degrees. Measure of angle B = (3 x) degrees. Measure of angle C = (4 x) degrees. Which statement is true about the angles? Measure of angle A = 20 degrees Measure of angle B = 60 degrees Angle A and [&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-246800","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246800","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=246800"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246800\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246800"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246800"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}