{"id":35453,"date":"2023-10-23T20:19:13","date_gmt":"2023-10-23T14:49:13","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=35453"},"modified":"2023-11-10T11:57:44","modified_gmt":"2023-11-10T06:27:44","slug":"related-angles","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/related-angles\/","title":{"rendered":"Related Angles &#8211; Interior, Exterior, Corresponding Angles"},"content":{"rendered":"<p>Related angles are nothing but the pairs of angles and assigned with specific names that we come across. Related angles have some conditions to mention. Learn the detailed concept of Related angles with images and examples in this article. Improve your preparation level by reading the entire concept without missing any subtopic. We have given complete information about <a href=\"https:\/\/ccssmathanswers.com\/lines-and-angles\/\"><strong>Lines and Angles<\/strong><\/a> on our website for free of cost.<\/p>\n<h2>Different Types of Related Angles<\/h2>\n<p>Check different types of Related Angles along with examples to clearly understand the concept. We have explained each of them with definitions, solved examples, etc. Refer to the following modules and get a grip on it.<\/p>\n<h3>Complementary Angles<\/h3>\n<p>If the sum of the measures of two angles is about 90\u00b0, those angles are called complementary angles.<\/p>\n<h4>Facts of Complementary Angles<\/h4>\n<ul>\n<li>The two right angles never complement each other.<\/li>\n<li>Also, the two obtuse angles never complement each other.<\/li>\n<li>Two complementary angles are always acute but there is no possibility of vice versa.<\/li>\n<\/ul>\n<p>Example:<\/p>\n<p>Let us take two angles which are complementary angles. If one angle is a, then the other angle is 90\u00b0 &#8211; a.<br \/>\nAn angle of 40\u00b0 and another angle of 50\u00b0 are complementary angles of each other.<\/p>\n<p>Also, complement of 40\u00b0 is 90\u00b0 &#8211; 40\u00b0 = 50\u00b0.<br \/>\nAnd complement of 50\u00b0 is 90\u00b0 &#8211; 50\u00b0 = 40\u00b0<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-6983\" src=\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/Complementary-angle.jpg\" alt=\"Complementary angle\" width=\"253\" height=\"156\" \/><\/p>\n<p>The \u2220XOY is 40\u00b0 and \u2220MON is 50\u00b0. By adding two angles \u2220XOY and \u2220MON, we get 90\u00b0 as they are the Complementary Angles.<\/p>\n<p>Therefore, the sum of the \u2220XOY and \u2220MON is 90\u00b0<br \/>\n\u2220XOY + \u2220MON = 90\u00b0.<\/p>\n<h3>Supplementary Angles<\/h3>\n<p>Supplementary Angles are the angles when the sum of the measures of two angles is 180\u00b0. If the sum of the two angles forms a straight angle, then those angles are called Supplementary Angles. If one angle is a, then the other angle is 180\u00b0 &#8211; a.<\/p>\n<p>Example:<\/p>\n<p>Let us take two angles which are Supplementary angles. If one angle is x, then the other angle is 180\u00b0 &#8211; x.<br \/>\nAn angle of 110\u00b0 and another angle of 70\u00b0 are supplementary angles of each other. Also, a supplement of 110\u00b0 is 180\u00b0 &#8211; 110\u00b0 = 70\u00b0.<br \/>\nAnd the supplement of 60\u00b0 is 180\u00b0 &#8211; 70\u00b0 = 110\u00b0.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-6985\" src=\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/Supplementary-angle-300x161.jpg\" alt=\"Supplementary angle\" width=\"257\" height=\"138\" \/><\/p>\n<p>From the above figure, the \u2220XOY is 110\u00b0 and \u2220MON is 70\u00b0. By adding two angles \u2220XOY and \u2220MON, we get 180\u00b0 as they are the Supplementary Angles.<\/p>\n<p>Therefore, the sum of the \u2220XOY and \u2220MON is 180\u00b0<br \/>\n\u2220XOY + \u2220MON = 180\u00b0.<\/p>\n<h3>Adjacent Angles<\/h3>\n<p>The two angles are called to be Adjacent angles when they have a common arm, a common vertex, and also the non-common arms present on the opposite side of the common arm.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-6992\" src=\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/Adjacent-angle.jpg\" alt=\"Adjacent angle\" width=\"166\" height=\"129\" \/><\/p>\n<p>From the above figure, \u2220ABD and \u2220CBD are adjacent angles with the common arm BD. The B is the common vertex and BA, BC is opposite sides of BD.<\/p>\n<h3>Linear Pair<\/h3>\n<p>When two adjacent angles form a linear pair of angles with the non-common arms are two opposite rays. In other words, the sum of two adjacent angles is 180\u00b0.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-7012\" src=\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/linear-pair-of-angles-300x205.jpg\" alt=\"linear pair of angles\" width=\"236\" height=\"161\" \/><\/p>\n<p>From the above figure, the \u2220XOY and \u2220XOZ are two adjacent angles. By adding two angles \u2220XOY and \u2220XOZ, we get 180\u00b0.<\/p>\n<p>Therefore, the sum of the \u2220XOY and \u2220XOZ is 180\u00b0<br \/>\n\u2220XOY + \u2220XOZ = 180\u00b0.<\/p>\n<h3>Vertically Opposite Angles<\/h3>\n<p>The arms of the lines are opposite in direction and both lines are interesting to each other in Vertically opposite angles. The pair of vertically opposite angles are equal.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-7013\" src=\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/vertically-opposite-angle.jpg\" alt=\"vertically opposite angles\" width=\"228\" height=\"143\" \/><\/p>\n<p>From the above figure, the \u2220MOR and \u2220SON and \u2220MOS and \u2220RON are pairs of vertically opposite angles.<\/p>\n<h3>Theorems on Related Angles<\/h3>\n<p>1. If a ray stands on a line, then the sum of adjacent angles formed is 180\u00b0.<\/p>\n<p>Given: A ray BE standing on (AC) \u20e1 such that \u2220ABE and \u2220CBE are formed.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-7014\" src=\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/sum-of-adjacent-angles-300x222.jpg\" alt=\"sum-of-adjacent-angles\" width=\"245\" height=\"181\" \/><\/p>\n<p>Construction: Draw BD \u22a5 AC.<\/p>\n<p>Proof: Take the angle ABE.<br \/>\nNow \u2220ABE = \u2220ABD + \u2220DBE \u2026\u2026\u2026\u2026\u2026. (1)<br \/>\nTake the angle CBE.<br \/>\nAlso \u2220CBE = \u2220CBD &#8211; \u2220DBE \u2026\u2026\u2026\u2026\u2026. (2)<br \/>\nNow, add equation 1 and equation 2.<br \/>\nAdding (1) and (2),<br \/>\n\u2220ABE + \u2220CBE = \u2220ABD + \u2220CBD + \u2220DBE &#8211; \u2220DBE<br \/>\n\u2220DBE &#8211; \u2220DBE = 0<br \/>\n= \u2220ABD + \u2220CBD<br \/>\n\u2220ABD = 90\u00b0; \u2220CBD = 90\u00b0<br \/>\nSubstitute \u2220ABD and \u2220CBD values in \u2220ABD + \u2220CBD<br \/>\n= 90\u00b0 + 90\u00b0<br \/>\n= 180\u00b0<\/p>\n<p>2. The sum of all the angles around a point is equal to 360\u00b0.<\/p>\n<p>Given: A point O and rays OA, OB, OC, OD, OE which make angles around O.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-7015\" src=\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/angles-around-a-point.jpg\" alt=\"angles-around-a-point\" width=\"185\" height=\"140\" \/><\/p>\n<p>Construction: Draw OD opposite to ray OA<\/p>\n<p>Proof: Since, OB stands on DA therefore<br \/>\n\u2220AOB + \u2220BOD = 180\u00b0<br \/>\n\u2220BOD = \u2220BOC + \u2220COD<br \/>\nSubstitute \u2220BOD = \u2220BOC + \u2220COD in \u2220AOB + \u2220BOD = 180\u00b0<br \/>\n\u2220AOB + (\u2220BOC + \u2220COD) = 180\u00b0<br \/>\n\u2220AOB + \u2220BOC + \u2220COD = 180\u00b0 \u2026\u2026\u2026\u2026\u2026. (i)<br \/>\nAgain OE stands on DA, therefore<br \/>\n\u2220DOE + \u2220EOA = 180\u00b0<br \/>\n\u2220EOA = \u2220EOF + \u2220FOA<br \/>\nSubstitute \u2220EOA = \u2220EOF + \u2220FOA in \u2220DOE + \u2220EOA = 180\u00b0<br \/>\n\u2220DOE + (\u2220EOF + \u2220FOA) = 180\u00b0<br \/>\n\u2220DOE + \u2220EOF + \u2220FOA = 180\u00b0 \u2026\u2026\u2026\u2026\u2026. (ii)<br \/>\nNow, add euqtion (i) and equation (ii)<br \/>\nAdding (i) and (ii),<br \/>\n\u2220AOB + \u2220BOC + \u2220COD + \u2220DOE + \u2220EOF + \u2220FOA<br \/>\n= 180\u00b0 + 180\u00b0<br \/>\n= 360\u00b0<\/p>\n<p>3. If two lines intersect, then vertically opposite angles are equal.<\/p>\n<p>Given: MN and AB intersect at point O.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-7016\" src=\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/vertically-opposite.jpg\" alt=\"vertically-opposite\" width=\"235\" height=\"126\" \/><\/p>\n<p>Proof: OB stands on MN.<br \/>\nTherefore, \u2220MOB + \u2220BON = 180\u00b0 \u2026\u2026\u2026\u2026\u2026. (i)<br \/>\nMO stands on AB<br \/>\n\u2220MOB + \u2220MOA = 180\u00b0 \u2026\u2026\u2026\u2026\u2026. (ii)<br \/>\nFrom (i) and (ii),<br \/>\n\u2220MOB + \u2220BON = \u2220MOB + \u2220MOA<br \/>\n\u2220BON + \u2220MOA<br \/>\nSimilarly, \u2220MOB = \u2220AON can be proved.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Related angles are nothing but the pairs of angles and assigned with specific names that we come across. Related angles have some conditions to mention. Learn the detailed concept of Related angles with images and examples in this article. Improve your preparation level by reading the entire concept without missing any subtopic. We have given &#8230; <a title=\"Related Angles &#8211; Interior, Exterior, Corresponding Angles\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/related-angles\/\" aria-label=\"More on Related Angles &#8211; Interior, Exterior, Corresponding 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\/35453"}],"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=35453"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35453\/revisions"}],"predecessor-version":[{"id":92642,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35453\/revisions\/92642"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=35453"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=35453"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=35453"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}