{"id":35467,"date":"2023-10-23T20:24:12","date_gmt":"2023-10-23T14:54:12","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=35467"},"modified":"2023-11-10T11:56:49","modified_gmt":"2023-11-10T06:26:49","slug":"complementary-and-supplementary-angles","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/complementary-and-supplementary-angles\/","title":{"rendered":"Complementary and Supplementary Angles Definition, Examples | How to find Complementary, Supplementary Angles?"},"content":{"rendered":"<p>Complementary and Supplementary Angles are the angles formed by adding two angles. If the sum of the two angles is 90\u00ba, they are called Complementary angles. Or else, if the sum of the two angles is 180\u00ba, they are called Supplementary angles. Find different problems on Supplementary and Complementary Angles in this article. Also, we have given all the concepts available in <a href=\"https:\/\/ccssmathanswers.com\/lines-and-angles\/\"><strong>Lines and Angles<\/strong><\/a> on our website.<\/p>\n<h3>Complementary Angles<\/h3>\n<p>The two angles are said to be complementary angles if their sum is one right angle i.e. 90\u00b0. Each angle is called the complement of the other. If x\u00b0 is one angle then (90 &#8211; x)\u00b0 is the other angle in Complementary Angles.<\/p>\n<p>For example, if 70\u00b0 is one angle in Complementary Angles, then the other angle will be 20\u00b0. 70\u00b0 and 20\u00b0 complement each other.<\/p>\n<p>Example 1: To find the complement of 3y + 52\u00b0, subtract the given angle from 90 degrees.<br \/>\n90\u00ba \u2013 (3y + 52\u00ba) = 90\u00ba \u2013 3y \u2013 52\u00ba = -3y + 38\u00ba<\/p>\n<p>The complement of 3y + 52\u00b0 is 38\u00ba \u2013 3y.<\/p>\n<h4>Facts of complementary angles<\/h4>\n<ul>\n<li>Two complementary angles are acute but vice versa is not possible<\/li>\n<li>Two right angles cannot complement each other<\/li>\n<li>Also, two obtuse angles cannot complement each other<\/li>\n<\/ul>\n<h3>Supplementary Angles<\/h3>\n<p>The two angles are said to be Supplementary angles if their sum is 180\u00b0. Two angles are added and formed a straight line in Supplementary Angles. If x is one angle then (180 &#8211; x)\u00b0 is the other angle in Supplementary Angles.<\/p>\n<p>For example, if 130\u00b0 is one angle in Supplementary Angles, then the other angle will be 50\u00b0. By adding 130 and 50 degrees, it forms a straight line. In Supplementary Angles, both angles are said to be a supplement to each other.<\/p>\n<h3>Solved Examples on Supplementary and Complementary Angles<\/h3>\n<p>1. Find the complement of 50 degrees?<\/p>\n<p>Solution:<br \/>\nThe given angle is 50 degrees, then, the Complement is 40 degrees.<br \/>\nWe know that Sum of Complementary angles = 90 degrees.<br \/>\nBy adding 40 degrees to 50 degrees, the total angle becomes 90 degrees.<br \/>\nSo, 50\u00b0 + 40\u00b0 = 90\u00b0<\/p>\n<p>The final answer is 90\u00b0<\/p>\n<p>2. Find the Supplement of the angle 1\/4 of 200\u00b0.<\/p>\n<p>Solution:<br \/>\nGiven that the angle 1\/4 of 200\u00b0<br \/>\nConvert 1\/4 of 200\u00b0<br \/>\nThat is, 1\/4 x 200\u00b0 = 50\u00b0<br \/>\nSupplement of 50\u00b0 = 180\u00b0 \u2013 50\u00b0 = 130\u00b0<br \/>\nBy adding 130 degrees to 50 degrees, the total angle becomes 180 degrees.<\/p>\n<p>Therefore, Supplement of the angle 1\/4 of 200\u00b0 is 130\u00b0<\/p>\n<p>3. The measures of two angles are (x + 15)\u00b0 and (3x + 25)\u00b0. Find the value of x if angles are supplementary angles.<\/p>\n<p>Solution:<br \/>\nWe know that, Sum of Supplementary angles = 180 degrees.<br \/>\nSo, (x + 15)\u00b0 + (3x + 25)\u00b0 = 180\u00b0<br \/>\nAdd the x terms and numbers.<br \/>\n4x + 40\u00b0 = 180\u00b0<br \/>\nMove 40\u00b0 to the right side and subtract it from 180\u00b0.<br \/>\n4x = 140\u00b0<br \/>\nMove 4 to the right side and divide it from 140\u00b0.<br \/>\nx = 35\u00b0<\/p>\n<p>The value of x is 35 degrees.<\/p>\n<p>4. The difference between two complementary angles is 54\u00b0. Find both the angles.<\/p>\n<p>Solution:<br \/>\nGiven that the difference between two complementary angles is 54\u00b0.<br \/>\nLet, the first angle = x degrees, then, Second angle = (90 \u2013 x)degrees {as per the definition of complementary angles}<br \/>\nDifference between angles = 54\u00b0<br \/>\nNow, (90\u00b0 \u2013 x) \u2013 x = 54\u00b0<br \/>\n90\u00b0 \u2013 2x = 54\u00b0<br \/>\n\u2013 2x = 54\u00b0 \u2013 90\u00b0<br \/>\n-2x = -36\u00b0<br \/>\nx = 36\u00b0\/2\u00b0<br \/>\nx = 18\u00b0<br \/>\nAgain, Second angle = 90\u00b0 \u2013 18\u00b0 = 72\u00b0<\/p>\n<p>Therefore, the required angles are 18\u00b0, 72\u00b0.<\/p>\n<p>5. Find the complement of the angle 4\/5 of 90\u00b0.<\/p>\n<p>Solution:<br \/>\nConvert 4\/5 of 90\u00b0<br \/>\nMultiply 4\/5 with 90\u00b0<br \/>\n4\/5 \u00d7 90\u00b0 = 72\u00b0<br \/>\nComplement of 72\u00b0 = 90\u00b0 &#8211; 72\u00b0 = 18\u00b0<\/p>\n<p>Therefore, a complement of the angle 4\/5 of 90\u00b0 = 18\u00b0<\/p>\n<p>6. Find the supplement of the angle 2\/3 of 90\u00b0.<\/p>\n<p>Solution:<br \/>\nConvert 2\/3 of 90\u00b0<br \/>\n2\/3 \u00d7 90\u00b0 = 60\u00b0<br \/>\nSupplement of 60\u00b0 = 180\u00b0 &#8211; 60\u00b0 = 120\u00b0<\/p>\n<p>Therefore, a supplement of the angle 2\/3 of 90\u00b0 = 120\u00b0<\/p>\n<p>7. The measure of two complementary angles are (3x &#8211; 6)\u00b0 and (x &#8211; 4)\u00b0. Find the value of x.<\/p>\n<p>Solution:<br \/>\nAccording to the problem, (3x &#8211; 6)\u00b0 and (x &#8211; 4)\u00b0, are complementary angles\u2019 so we get;<br \/>\n(3x &#8211; 6)\u00b0 + (x &#8211; 4)\u00b0 = 90\u00b0<br \/>\nor, 3x &#8211; 6\u00b0 + x &#8211; 4\u00b0 = 90\u00b0<br \/>\nor, 3x + x &#8211; 6\u00b0 &#8211; 4\u00b0 = 90\u00b0<br \/>\nor, 4x &#8211; 10\u00b0 = 90\u00b0<br \/>\nAdd 10\u00b0 on both sides.<br \/>\nor, 4x &#8211; 10\u00b0 + 10\u00b0 = 90\u00b0 + 10\u00b0<br \/>\nor, 4x = 100\u00b0<br \/>\nor, x = 100\u00b0\/4\u00b0<br \/>\nor, x = 25\u00b0<\/p>\n<p>Therefore, the value of x = 25\u00b0.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Complementary and Supplementary Angles are the angles formed by adding two angles. If the sum of the two angles is 90\u00ba, they are called Complementary angles. Or else, if the sum of the two angles is 180\u00ba, they are called Supplementary angles. Find different problems on Supplementary and Complementary Angles in this article. Also, we &#8230; <a title=\"Complementary and Supplementary Angles Definition, Examples | How to find Complementary, Supplementary Angles?\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/complementary-and-supplementary-angles\/\" aria-label=\"More on Complementary and Supplementary Angles Definition, Examples | How to find Complementary, Supplementary Angles?\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35467"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=35467"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35467\/revisions"}],"predecessor-version":[{"id":92638,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35467\/revisions\/92638"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=35467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=35467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=35467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}