{"id":232789,"date":"2025-06-12T07:26:56","date_gmt":"2025-06-12T07:26:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232789"},"modified":"2025-06-12T07:26:58","modified_gmt":"2025-06-12T07:26:58","slug":"find-the-measure-of-each-marked-angle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/find-the-measure-of-each-marked-angle\/","title":{"rendered":"Find the measure of each marked angle."},"content":{"rendered":"\n

1. The degree measure of the top angle of the triangle, with angle measure (3x-26) is . 2. The degree measure of the bottom left angle of the triangle, with angle measure (x+9) is <\/em>. 3. The angle with measure (7x-125) that is supplementary to the last interior angle of the triangle is __<\/em><\/p>\n\n\n\n

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

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

 The degree measure of the top angle of the triangle, with angle measure (3x-26)\u00b0, is 82\u00b0.<\/strong>
2. The degree measure of the bottom left angle of the triangle, with angle measure (x+9)\u00b0, is 45\u00b0.<\/strong>
3. The angle with measure (7x-125)\u00b0, that is supplementary to the last interior angle of the triangle is 127\u00b0.<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To determine the measure of each angle, we must first find the value of x<\/em>. The solution relies on the Exterior Angle Theorem<\/strong>, a fundamental concept in geometry. This theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two non-adjacent (or remote) interior angles.<\/p>\n\n\n\n

Step 1: Set up the equation<\/strong><\/p>\n\n\n\n

Based on the provided image, we can identify the following angles:<\/p>\n\n\n\n

    \n
  • The two remote interior angles are the top angle,\u00a0(3x – 26)\u00b0<\/strong>, and the bottom-left angle,\u00a0(x + 9)\u00b0<\/strong>.<\/li>\n\n\n\n
  • The exterior angle at the bottom-right vertex is\u00a0(7x – 125)\u00b0<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    Applying the Exterior Angle Theorem, we set the sum of the two remote interior angles equal to the exterior angle:
    (3x – 26) + (x + 9) = 7x – 125<\/p>\n\n\n\n

    Step 2: Solve the equation for x<\/strong><\/p>\n\n\n\n

    First, combine the like terms on the left side of the equation:
    4x – 17 = 7x – 125<\/p>\n\n\n\n

    Next, isolate the variable x<\/em>. We can do this by subtracting 4x from both sides:
    -17 = 3x – 125<\/p>\n\n\n\n

    Then, add 125 to both sides to isolate the term with x<\/em>:
    108 = 3x<\/p>\n\n\n\n

    Finally, divide by 3 to find the value of x<\/em>:
    x = 36<\/strong><\/p>\n\n\n\n

    Step 3: Calculate the measure of each angle<\/strong><\/p>\n\n\n\n

    Now that we have the value of x<\/em>, we can substitute it back into the expressions for each angle:<\/p>\n\n\n\n

      \n
    1. Top Angle:<\/strong>
      (3x – 26)\u00b0 = 3(36) – 26 = 108 – 26 =\u00a082\u00b0<\/strong><\/li>\n\n\n\n
    2. Bottom Left Angle:<\/strong>
      (x + 9)\u00b0 = 36 + 9 =\u00a045\u00b0<\/strong><\/li>\n\n\n\n
    3. Exterior Angle (supplementary to the bottom right interior angle):<\/strong>
      (7x – 125)\u00b0 = 7(36) – 125 = 252 – 125 =\u00a0127\u00b0<\/strong><\/li>\n<\/ol>\n\n\n\n

      As a final check, the third interior angle is 180\u00b0 – 127\u00b0 = 53\u00b0. The sum of the three interior angles is 82\u00b0 + 45\u00b0 + 53\u00b0 = 180\u00b0, which confirms the calculations are correct.<\/p>\n\n\n\n

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

      1. The degree measure of the top angle of the triangle, with angle measure (3x-26) is . 2. The degree measure of the bottom left angle of the triangle, with angle measure (x+9) is . 3. The angle with measure (7x-125) that is supplementary to the last interior angle of the triangle is __ The […]<\/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-232789","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232789","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=232789"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232789\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}