{"id":27363,"date":"2025-06-19T22:31:53","date_gmt":"2025-06-19T22:31:53","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=27363"},"modified":"2025-06-19T22:31:54","modified_gmt":"2025-06-19T22:31:54","slug":"in-triangle-fgh-the-measure-of-angle-f-is-twice-as-large-as-the-measure-of-angle-g-and-the-measure-of-angle-g-is-3-times-the-measure-of-angle-h","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/in-triangle-fgh-the-measure-of-angle-f-is-twice-as-large-as-the-measure-of-angle-g-and-the-measure-of-angle-g-is-3-times-the-measure-of-angle-h\/","title":{"rendered":"In triangle FGH, the measure of angle F is twice as large as the measure of angle G and the measure of angle G is 3 times the measure of angle H."},"content":{"rendered":"\n<p>In triangle FGH, the measure of angle F is twice as large as the measure of angle G and the measure of angle G is 3 times the measure of angle H. Find the measure of angle G<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-light-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given a triangle FGH with the following relationships between the angles:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The measure of angle F is <strong>twice<\/strong> the measure of angle G<\/li>\n\n\n\n<li>The measure of angle G is <strong>three times<\/strong> the measure of angle H<\/li>\n<\/ul>\n\n\n\n<p>Let us use algebra to find the measure of angle G.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Define the unknown<\/h3>\n\n\n\n<p>Let the measure of angle H be <strong>x<\/strong> degrees.<\/p>\n\n\n\n<p>From the given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angle G is 3 times angle H \u2192 G = <strong>3x<\/strong><\/li>\n\n\n\n<li>Angle F is twice angle G \u2192 F = <strong>2 \u00d7 3x = 6x<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Use the triangle angle sum rule<\/h3>\n\n\n\n<p>In any triangle, the sum of the interior angles is always <strong>180 degrees<\/strong>. So:<\/p>\n\n\n\n<p>F + G + H = 180<br>Substitute the expressions:<\/p>\n\n\n\n<p>6x + 3x + x = 180<br>Combine like terms:<\/p>\n\n\n\n<p>10x = 180<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solve for x<\/h3>\n\n\n\n<p>Divide both sides by 10:<br>x = 18<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Find the measure of angle G<\/h3>\n\n\n\n<p>We had defined G = 3x<br>So G = 3 \u00d7 18 = <strong>54 degrees<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p><strong>The measure of angle G is 54 degrees.<\/strong><\/p>\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>To solve problems involving angles in a triangle, it is essential to remember that the sum of the interior angles in any triangle is always 180 degrees. This property provides a reliable equation that can be used in combination with given relationships between the angles.<\/p>\n\n\n\n<p>In this triangle FGH, we were told that angle F is twice the size of angle G, and angle G is three times the size of angle H. By assigning a variable to the smallest angle (angle H), we set H = x. This made it easier to express the other angles in terms of x: G = 3x and F = 6x. This approach simplifies complex word problems and allows us to reduce everything to a single variable.<\/p>\n\n\n\n<p>Once the angles were expressed in terms of x, the next step was to use the triangle angle sum rule. Adding the expressions for F, G, and H and setting the sum equal to 180 gave us a solvable equation: 6x + 3x + x = 180. Solving that gave us x = 18, which represents angle H.<\/p>\n\n\n\n<p>From there, we used the value of x to find the measure of angle G, which is 3x. Multiplying 18 by 3 gave us 54 degrees.<\/p>\n\n\n\n<p>This method demonstrates the power of algebra in solving geometric problems and shows the importance of understanding relationships between angles in a triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-130.jpeg\" alt=\"\" class=\"wp-image-27367\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-130.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-130-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In triangle FGH, the measure of angle F is twice as large as the measure of angle G and the measure of angle G is 3 times the measure of angle H. Find the measure of angle G The Correct Answer and Explanation is: We are given a triangle FGH with the following relationships between [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-27363","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27363","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=27363"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27363\/revisions"}],"predecessor-version":[{"id":27369,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27363\/revisions\/27369"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}