{"id":232794,"date":"2025-06-12T07:34:40","date_gmt":"2025-06-12T07:34:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232794"},"modified":"2025-06-12T07:34:42","modified_gmt":"2025-06-12T07:34:42","slug":"in-the-triangle-below-suppose-that-m%e2%88%a0hx9degree-m%e2%88%a0i2x%e2%88%925degree-and-m%e2%88%a0j5xdegree","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/in-the-triangle-below-suppose-that-m%e2%88%a0hx9degree-m%e2%88%a0i2x%e2%88%925degree-and-m%e2%88%a0j5xdegree\/","title":{"rendered":"In the triangle below, suppose that\u00a0m\u2220H=(x+9)\\degree,\u00a0m\u2220I=(2x\u22125)\\degree, and\u00a0m\u2220J=(5x)\\degree"},"content":{"rendered":"\n
In the triangle below, suppose that\u00a0m\u2220H=(x+9)\\degree,\u00a0m\u2220I=(2x\u22125)\\degree, and\u00a0m\u2220J=(5x)\\degree. Find the degree measure of each angle in the triangle.<\/pre>\n\n\n\n

<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Here are the degree measures of each angle in the triangle:
m\u2220H = 31\u00b0<\/strong>
m\u2220I = 39\u00b0<\/strong>
m\u2220J = 110\u00b0<\/strong><\/p>\n\n\n\n
\n\n\n\n
Explanation<\/strong><\/h3>\n\n\n\n
This problem requires finding the measure of each interior angle of a triangle when the angles are given as algebraic expressions. The solution is based on the fundamental geometric principle known as the Triangle Angle-Sum Theorem<\/strong>. This theorem states that the sum of the measures of the three interior angles of any triangle is always 180 degrees.<\/p>\n\n\n\n
Step 1: Set up the equation.<\/strong>
According to the Triangle Angle-Sum Theorem, the sum of the measures of angles H, I, and J must equal 180\u00b0. This can be written as an equation:
m\u2220H + m\u2220I + m\u2220J = 180\u00b0<\/p>\n\n\n\n
By substituting the given expressions for each angle into this equation, the following algebraic relationship is established:
(x + 9) + (2x – 5) + (5x) = 180<\/p>\n\n\n\n
Step 2: Solve the equation for x.<\/strong>
To find the value of x, the equation must be simplified by combining like terms. First, combine all terms containing the variable x:
x + 2x + 5x = 8x<\/p>\n\n\n\n
Next, combine the constant terms:
9 – 5 = 4<\/p>\n\n\n\n
The simplified equation is now:
8x + 4 = 180<\/p>\n\n\n\n
To isolate the variable, subtract 4 from both sides of the equation:
8x = 180 – 4
8x = 176<\/p>\n\n\n\n
Finally, divide both sides by 8 to solve for x:
x = 176 \/ 8
x = 22<\/p>\n\n\n\n
Step 3: Calculate the measure of each angle.<\/strong>
Now that the value of x is known, it can be substituted back into the original expression for each angle to find its specific degree measure.<\/p>\n\n\n\n
    \n
  • For m\u2220H:<\/strong>
    m\u2220H = (x + 9)\u00b0
    m\u2220H = (22 + 9)\u00b0
    m\u2220H = 31\u00b0<\/strong><\/li>\n\n\n\n
  • For m\u2220I:<\/strong>
    m\u2220I = (2x – 5)\u00b0
    m\u2220I = (2 * 22 – 5)\u00b0
    m\u2220I = (44 – 5)\u00b0
    m\u2220I = 39\u00b0<\/strong><\/li>\n\n\n\n
  • For m\u2220J:<\/strong>
    m\u2220J = (5x)\u00b0
    m\u2220J = (5 * 22)\u00b0
    m\u2220J = 110\u00b0<\/strong><\/li>\n<\/ul>\n\n\n\n
    To verify the solution, check if the sum of the calculated angle measures is 180\u00b0:
    31\u00b0 + 39\u00b0 + 110\u00b0 = 70\u00b0 + 110\u00b0 = 180\u00b0.
    The sum is correct, confirming the accuracy of the results.thumb_upthumb_down<\/p>\n\n\n\n
    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
    In the triangle below, suppose that\u00a0m\u2220H=(x+9)\\degree,\u00a0m\u2220I=(2x\u22125)\\degree, and\u00a0m\u2220J=(5x)\\degree. Find the degree measure of each angle in the triangle. The Correct Answer and Explanation is: Here are the degree measures of each angle in the triangle:m\u2220H = 31\u00b0m\u2220I = 39\u00b0m\u2220J = 110\u00b0 Explanation This problem requires finding the measure of each interior angle of a triangle when […]<\/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-232794","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232794","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=232794"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232794\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232794"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}