{"id":235418,"date":"2025-06-15T11:08:29","date_gmt":"2025-06-15T11:08:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235418"},"modified":"2025-06-15T11:08:31","modified_gmt":"2025-06-15T11:08:31","slug":"find-the-measure-of-the-angle-indicated-in-bold","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/find-the-measure-of-the-angle-indicated-in-bold\/","title":{"rendered":"Find the measure of the angle indicated in bold."},"content":{"rendered":"\n

Find the measure of the angle indicated in bold. 13) x + 101 16 + x 14) 12x – 4 15x – 5<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Based on the images provided, here are the solutions to the geometry problems.<\/p>\n\n\n\n

Problem 13<\/strong><\/h3>\n\n\n\n

The angle indicated in bold is the one with the expression x + 101<\/strong>.<\/p>\n\n\n\n

Answer:<\/strong> The measure of the angle is 95 degrees<\/strong>.<\/p>\n\n\n\n

Explanation:<\/strong>
In this diagram, two angles, labeled with the expressions x + 101 and x + 91, are adjacent to each other on a straight line. Angles that form a straight line are known as a linear pair, and their measures are supplementary, meaning they add up to 180 degrees.<\/p>\n\n\n\n

To find the value of x, an equation can be set up by adding the two expressions and setting the sum equal to 180:
(x + 101) + (x + 91) = 180<\/p>\n\n\n\n

First, combine the like terms on the left side of the equation:
2x + 192 = 180<\/p>\n\n\n\n

Next, isolate the term with x by subtracting 192 from both sides of the equation:
2x = 180 – 192
2x = -12<\/p>\n\n\n\n

Finally, solve for x by dividing both sides by 2:
x = -6<\/p>\n\n\n\n

Now that the value of x is known, it can be substituted back into the expression for the bolded angle, x + 101:
Measure = (-6) + 101
Measure = 95<\/p>\n\n\n\n

Therefore, the measure of the angle indicated in bold is 95 degrees. The other angle would be (-6) + 91 = 85 degrees. As a check, 95 + 85 = 180, which confirms the calculations are correct.<\/p>\n\n\n\n

\n\n\n\n

Problem 14<\/strong><\/h3>\n\n\n\n

The angle indicated in bold is the one with the expression 15x – 5<\/strong>.<\/p>\n\n\n\n

Answer:<\/strong> The measure of the angle is 100 degrees<\/strong>.<\/p>\n\n\n\n

Explanation:<\/strong>
This problem shows two parallel lines intersected by a transversal line. The two angles, labeled 12x – 4 and 15x – 5, are located between the parallel lines and on the same side of the transversal. This relationship identifies them as consecutive interior angles (or same-side interior angles). A property of parallel lines states that consecutive interior angles are supplementary, so their measures sum to 180 degrees.<\/p>\n\n\n\n

This relationship allows for the creation of the following equation:
(12x – 4) + (15x – 5) = 180<\/p>\n\n\n\n

Begin by combining the like terms on the left side:
27x – 9 = 180<\/p>\n\n\n\n

To solve for x, first add 9 to both sides of the equation:
27x = 189<\/p>\n\n\n\n

Then, divide both sides by 27 to find the value of x:
x = 7<\/p>\n\n\n\n

With the value of x determined, substitute it into the expression for the bolded angle, 15x – 5:
Measure = 15(7) – 5
Measure = 105 – 5
Measure = 100<\/p>\n\n\n\n

The measure of the angle indicated in bold is 100 degrees. The other angle’s measure is 12(7) – 4 = 84 – 4 = 80 degrees. The sum of these two angles is 100 + 80 = 180, which validates the supplementary relationship and the final answer.thumb_upthumb_down<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Find the measure of the angle indicated in bold. 13) x + 101 16 + x 14) 12x – 4 15x – 5 The Correct Answer and Explanation is: Based on the images provided, here are the solutions to the geometry problems. Problem 13 The angle indicated in bold is the one with the expression x […]<\/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-235418","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235418","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=235418"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235418\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235418"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}