{"id":143,"date":"2021-11-25T14:40:50","date_gmt":"2021-11-25T14:40:50","guid":{"rendered":"https:\/\/visualfractions.com\/blog\/?p=143"},"modified":"2023-02-23T17:08:29","modified_gmt":"2023-02-23T17:08:29","slug":"supplementary-angles","status":"publish","type":"post","link":"https:\/\/visualfractions.com\/blog\/supplementary-angles\/","title":{"rendered":"Supplementary Angles"},"content":{"rendered":"\n<p>A supplementary angle is when the sum of any two angles is 180\u00b0. The supplementary angles always form a linear angle that is 180\u00b0 when joined. In other words, if angle 1 + angle 2 = 180\u00b0, angle 1 and angle 2 will be called supplementary angles.<\/p>\n\n\n\n<p>Let\u2019s understand it better with the help of an example:<\/p>\n\n\n\n<p>If we have a 130\u00b0 and 50\u00b0 angle, we know that added together results in 180\u00b0, which means they are supplementary angles.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Criteria for Supplementary Angles<\/h2>\n\n\n\n<p>Two angles can be called supplementary if:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><meta charset=\"utf-8\">One of its angles is an acute angle and other angle is an obtuse angle<\/li><li>Both of the angles are right angles<\/li><\/ul>\n\n\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"604\" height=\"358\" src=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-31.png\" alt=\"\" class=\"wp-image-160\" srcset=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-31.png 604w, https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-31-300x178.png 300w\" sizes=\"auto, (max-width: 604px) 100vw, 604px\" \/><\/figure>\n\n\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"594\" height=\"318\" src=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-32.png\" alt=\"\" class=\"wp-image-161\" srcset=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-32.png 594w, https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-32-300x161.png 300w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><\/figure>\n\n\n\n\n\n<p>As you go through, you will explore a world of supplementary angles with important applications in solving various geometric problems.<\/p>\n\n\n\n<p>Let&#8217;s look at some examples of supplementary angles to get a better understanding:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>150\u00b0 + 30\u00b0 = 180\u00b0<\/li><li>130\u00b0 + 50\u00b0 = 180\u00b0<\/li><li>96\u00b0 +84\u00b0 = 180\u00b0<\/li><li>120\u00b0 + 60\u00b0 = 180\u00b0<\/li><li>90\u00b0 + 90\u00b0 = 180\u00b0<\/li><\/ul>\n\n\n\n<p>Now when you look at the above examples you will find that there will always be an obtuse angle (150\u00b0, 130\u00b0, 96\u00b0, 120\u00b0) added with an acute angle (60\u00b0, 90\u00b0, 40\u00b0, 84\u00b0) or there will be a sum of two right angles (90\u00b0, 90\u00b0).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">How to Find a Supplementary Angle<\/h2>\n\n\n\n<p>Let&#8217;s try to find the supplementary angle measurement for each measured angle.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example 1<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-25.png\" alt=\"\" class=\"wp-image-146\" width=\"158\" height=\"81\" srcset=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-25.png 316w, https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-25-300x154.png 300w\" sizes=\"auto, (max-width: 158px) 100vw, 158px\" \/><\/figure>\n\n\n\n<p>[katex]X\u00b0 + 38\u00b0 = 180\u00b0[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]X\u00b0 = 180\u00b0 &#8211; 38\u00b0[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]X\u00b0 = 142\u00b0[\/katex]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example 2<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-26.png\" alt=\"\" class=\"wp-image-148\" width=\"255\" height=\"115\" srcset=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-26.png 510w, https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-26-300x135.png 300w\" sizes=\"auto, (max-width: 255px) 100vw, 255px\" \/><\/figure>\n\n\n\n<p><meta charset=\"utf-8\">[katex]Y\u00b0 + 77\u00b0 = 180\u00b0[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]Y\u00b0 = 180\u00b0 &#8211; 77\u00b0[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]Y\u00b0 = 103\u00b0[\/katex]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example 3<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-27.png\" alt=\"\" class=\"wp-image-149\" width=\"286\" height=\"107\" srcset=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-27.png 572w, https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-27-300x112.png 300w\" sizes=\"auto, (max-width: 286px) 100vw, 286px\" \/><\/figure>\n\n\n\n<p><meta charset=\"utf-8\">[katex]X\u00b0 + 130\u00b0 = 180\u00b0[\/katex]<\/p>\n\n\n\n<p>[katex]X\u00b0 = 180\u00b0 &#8211; 130\u00b0[\/katex]<\/p>\n\n\n\n<p>[katex]X\u00b0 = 50\u00b0[\/katex]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example 4<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-28.png\" alt=\"\" class=\"wp-image-150\" width=\"327\" height=\"96\" srcset=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-28.png 654w, https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-28-300x88.png 300w\" sizes=\"auto, (max-width: 327px) 100vw, 327px\" \/><\/figure>\n\n\n\n<p>[katex]X\u00b0 + 118\u00b0 = 180\u00b0[\/katex]<\/p>\n\n\n\n<p>[katex]X\u00b0 = 180\u00b0 &#8211; 118\u00b0[\/katex]<\/p>\n\n\n\n<p>[katex]X\u00b0 = 62\u00b0[\/katex]<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Properties of Supplementary Angles<\/h2>\n\n\n\n<p>Supplementary angles all share the same properties:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Any two angles are said to be supplementary angles when their sums add up to 180\u00b0<\/li><li>The &#8220;S&#8217; in supplementary angles stand for Straight line, this means that they form 180\u00b0<\/li><li>The supplementary angles do not have to be on the same line, they can be on different lines, but should measure 180\u00b0<\/li><li>In a supplementary angle if one angle is 90\u00b0, then the other angle will also be 90\u00b0.<\/li><\/ul>\n\n\n\n<p>When two supplementary angles are joined together, they form a straight line and a straight angle. But also note that even if two angles are supplementary to each other, they do not have to be next to each other. Hence, any two angles can be supplementary angles, if their sum is equivalent to 180<strong>\u00b0.<\/strong><\/p>\n\n\n\n<p><strong>One of the most asked questions is whether all supplementary angles form linear pairs?<\/strong><\/p>\n\n\n\n<p>Supplementary angles do not have to be adjacent, but linear pairs must be adjacent to form a straight line. So, remember that supplementary angles are not necessarily linear pairs. However, linear pairs are always supplementary.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Types of Supplementary Angles<\/h2>\n\n\n\n<p>Adjacent and non-adjacent supplementary angles are the two types of supplementary angles. Each of these types of supplementary angles is explained below.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Adjacent Supplementary Angles<\/h3>\n\n\n\n<p>Two supplementary angles that have a common vertex and a common arm are said to be adjacent supplementary angles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-29.png\" alt=\"\" class=\"wp-image-151\" width=\"360\" height=\"222\" srcset=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-29.png 720w, https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-29-300x185.png 300w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Example<\/h4>\n\n\n\n<p>Here \u2220 BOA and \u2220 AOC are adjacent angles as they have a common vertex, O, and a \u00b0common arm OA. These two angles add up to 180 degrees, that is \u2220 BOA + \u2220 AOC = 180\u00b0. Hence, these two angles can be called adjacent supplementary angles.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Non-Adjacent Supplementary Angles<\/h3>\n\n\n\n<p>Put simply, two supplementary angles that are not adjacent are said to be non-adjacent supplementary angles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-30.png\" alt=\"\" class=\"wp-image-152\" width=\"330\" height=\"150\" srcset=\"https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-30.png 660w, https:\/\/visualfractions.com\/blog\/wp-content\/uploads\/2021\/11\/image-30-300x136.png 300w\" sizes=\"auto, (max-width: 330px) 100vw, 330px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Example<\/h4>\n\n\n\n<p>Here, \u2220 ABC and \u2220 PQR are non-adjacent angles as they neither have a common nor a common arm. But when added up, that is 130\u00b0 + 50\u00b0 = 180\u00b0, their sum comes as 180\u00b0. Hence, they are supplementary angles but not adjacent. Note that, when two adjacent supplementary angles are put together, they form a straight line.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Supplementary Angles Formula<\/h2>\n\n\n\n<p>You can calculate supplementary angles by subtracting the specified angle from 180 degrees. To find other angles, use the following formula:<\/p>\n\n\n\n<p>[katex]\u2220x = 180\u00b0-\u2220y or \u2220y = 180\u00b0 -\u2220x[\/katex]<\/p>\n\n\n\n<p>Where <meta charset=\"utf-8\">\u2220x or \u2220y is the given angle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Supplementary Angles Theory<\/h2>\n\n\n\n<p>According to the supplementary angles theorem, if two angles are supplementary to the same angle, then they are congruent to each other.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Examples<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>Angle A + Angle B = 180\u00b0<\/li><li>Angle C + Angle B = 180\u00b0<\/li><\/ul>\n\n\n\n<p>Therefore, Angle A is congruent to Angle C.<\/p>\n\n\n\n<p>Now let&#8217;s go through some quick solved examples and test your knowledge:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example 1<\/h4>\n\n\n\n<p>There are two angles that are supplementary and one of the two angles is 50\u00b0. Find the other angle.<\/p>\n\n\n\n<p><strong>Solution<\/strong>: Let&#8217;s take the other angle to be \u2220 x.<\/p>\n\n\n\n<p>Now, given that the two angles are supplementary and we know that the sum of the measures of these two angles is 180 degrees so:<\/p>\n\n\n\n<p>[katex]\u2220 x + 50\u00b0 = 180\u00b0[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]\u2220 x = 180\u00b0 -50\u00b0[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]\u2220 x = 130\u00b0[\/katex]<\/p>\n\n\n\n<p>So, the other angle is 130\u00b0. Here One angle is obtuse i.e., 130\u00b0, and one is acute i.e., 50\u00b0.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example 2<\/h4>\n\n\n\n<p>Two angles are supplementary and one of them is 137\u00b0. What is the size of another angle?<\/p>\n\n\n\n<p>Say we have angle \u2220 b given i.e., 137\u00b0. Let&#8217;s take the other unknown angle to be \u2220 a.<\/p>\n\n\n\n<p>Now that we know that the sum of angles \u2220 a + \u2220 b will always be 180 degrees as it is a supplementary angle.<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]\u2220 a + 137\u00b0 = 180\u00b0[\/katex]<\/p>\n\n\n\n<p>So, the other angle is \u2220 a = 43\u00b0. Here, obtuse angle is 137\u00b0 and acute angle is 43\u00b0.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Supplementary Angles in Ratios<\/h2>\n\n\n\n<p>We can also work out supplementary angles in ratios.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p>Two supplementary angles are in the ratio 4: 5. Find the other angles?<\/p>\n\n\n\n<p>We know that supplementary angles add up to form 180<meta charset=\"utf-8\">\u00b0, so let&#8217;s find the other angles using the 4:5 ratio.<\/p>\n\n\n\n<p>First, we&#8217;ll call one angle 4x and the other 5x. Now we can put this into the supplementary angles formula.<\/p>\n\n\n\n<p>[katex]4x + 5x = 180\u00b0[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]9x = 180\u00b0[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]x + \\dfrac{180\u00b0}{9}[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">[katex]x = 20\u00b0[\/katex]<\/p>\n\n\n\n<p>Now we know that x is 20<meta charset=\"utf-8\">\u00b0, we can easily work out both angles in the ratio:<\/p>\n\n\n\n<p>&nbsp;[katex]4x = 4 \\times 20\u00b0 = 80\u00b0[\/katex]<\/p>\n\n\n\n<p><meta charset=\"utf-8\">&nbsp;[katex]5x = 5 \\times 20\u00b0 = 100\u00b0[\/katex]<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Supplementary Angles vs Complementary Angles<\/h2>\n\n\n\n<p>Sometimes, supplementary angles are confused with complementary angles. Let&#8217;s have a quick go through and find the differences between Supplementary and complementary angles, so that you never confuse the two.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th><meta charset=\"utf-8\"><strong>Supplementary Angles<\/strong><\/th><th><meta charset=\"utf-8\"><strong>Complementary Angles<\/strong><\/th><\/tr><\/thead><tbody><tr><td>The sum total of angles in supplementary angles is 180 degrees. &nbsp; &nbsp;<\/td><td>The sum total of complementary angles is always 90 degrees. &nbsp;<\/td><\/tr><tr><td>\u2220a + \u2220b = 180<\/td><td>\u2220a + \u2220 b = 90<\/td><\/tr><tr><td>The supplementary angles are in the form of a straight line.<\/td><td>The complementary angles are in the form of right angle &nbsp;<\/td><\/tr><tr><td>The supplement of any angle is 180 &#8211; the angle given.<\/td><td>The compliment of any angle is 90 &#8211; the angle given. &nbsp;<\/td><\/tr><tr><td>The sum total of angles in supplementary angles is 180 degrees.<\/td><td>The sum total of complementary angles is always 90 degrees. &nbsp; &nbsp;<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find out what supplementary angles are, the different types, and how to find and calculate them.<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-143","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/posts\/143","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/comments?post=143"}],"version-history":[{"count":11,"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/posts\/143\/revisions"}],"predecessor-version":[{"id":308,"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/posts\/143\/revisions\/308"}],"wp:attachment":[{"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/media?parent=143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/categories?post=143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/visualfractions.com\/blog\/wp-json\/wp\/v2\/tags?post=143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}