{"id":5584,"date":"2022-06-22T05:07:22","date_gmt":"2022-06-22T12:07:22","guid":{"rendered":"https:\/\/studysoup.com\/blog\/?p=5584"},"modified":"2022-06-22T05:07:22","modified_gmt":"2022-06-22T12:07:22","slug":"adjacent-angles-definition-examples","status":"publish","type":"post","link":"https:\/\/newblog.studysoup.com\/?p=5584","title":{"rendered":"What Are Adjacent Angles?"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/studysoup.com\/blog\/wp-content\/uploads\/2022\/06\/adjacent-angles-1024x683.jpg\" alt=\"ruler and notebook\" class=\"wp-image-5755\"\/><\/figure>\n\n\n\n<p>Adjacent angles are two angles which share a common side while also having a common vertex without overlapping.  <\/p>\n\n\n\n<p>If there is a lack of one of these properties, it is simply not an adjacent angle. In simple terms, they are two angles that are beside each other. Let&#8217;s break down the common terms we use when talking about them.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Other Important Definitions<\/h3>\n\n\n\n<p>Before getting into the details, here are other important definitions you should keep in mind:<\/p>\n\n\n\n<p><strong>\u2022Common vertex:<\/strong> a point of intersection that is shared by two or more rays or lines. <strong> <\/strong><\/p>\n\n\n\n<p><strong>\u2022Common side<\/strong>&nbsp;is one line, ray, or line segment used to create two angles sharing the same vertex. Both angles use the common side and one other side.<\/p>\n\n\n\n<p><strong>\u2022Ray <\/strong>is a line that has a fixed starting point but an undefined end point.<br><br><strong>\u2022Line Segment  <\/strong>is a line that has two endpoints.<br><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>What are the properties of adjacent angles?<\/strong><\/h2>\n\n\n\n<p>Now that we\u2019ve defined the basic idea of what they are, let\u2019s discuss how to identify them. Here are the six fundamental properties you need to know:<br><\/p>\n\n\n\n<p>\u2022They share a common side and vertex.<\/p>\n\n\n\n<p>\u2022They never overlap.<\/p>\n\n\n\n<p>\u2022There\u2019s always a non-common arm on both sides of the common arm.<\/p>\n\n\n\n<p>\u2022They can be complementary (measures adding up to 90\u02da) or supplementary (measures adding up to 180\u02da) if they share a common angle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>How To Identify Adjacent Angles<\/strong><\/h2>\n\n\n\n<p>There are two properties that can help you identify them easily: If they share a common side (arm) and vertex. If only one of these properties is satisfied in two angles, then they are not adjacent angles.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Examples<\/h3>\n\n\n\n<p>In the real world you can see many examples of adjacent angles like:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Two connected pieces of pizzas with the middle divider being the shared side.<\/li><li>The hour, minute, and second hands on a clock.<\/li><\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Linear Pairs<\/h4>\n\n\n\n<p>In geometry, one of the most common examples is a linear pair in which two angle measures add up to form a straight angle (180\u02d9). Here\u2019s an example:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/studysoup.com\/blog\/wp-content\/uploads\/2022\/04\/images.png\" alt=\"adjacent angles\" class=\"wp-image-5587\"\/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Frequently Asked Questions<\/strong><br><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Are adjacent angles congruent?<\/strong><\/h3>\n\n\n\n<p>They can sometimes be congruent. \u201cCongruent\u201d means exactly equal as far as shape and \u201cadjacent\u201d means \u201cnext to\u201d. So when two angles have the exact same angle measurement they are equal. But, if they don\u2019t, they would not be considered congruent.<br><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Are adjacent angles complementary?<\/strong><\/h3>\n\n\n\n<p>Adjacent and non-adjacent angles can be complementary if they add up to 90 degrees. Two angles are said to be complementary if they add up to 90 degrees.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Are adjacent angles equal to 180?<\/strong><\/h3>\n\n\n\n<p>Adjacent angles can equal to 180\u02d9, but not in all cases. As mentioned above, supplementary adjacent angles add up to 180\u02d9but if the adjacent angles are not linear pairs, then they won\u2019t add up to 180\u02d9.<br><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Solutions For Common Problems<\/strong><\/h2>\n\n\n\n<p>\u2022<a href=\"https:\/\/studysoup.com\/tsg\/1100884\/geometry-concepts-and-applications-student-edition-geometry-concepts-applic-1-edition-chapter-3-4-problem-1\">Draw and label two adjacent angles for which the sum of their measures is 90\u02d9<br><\/a>\u2022<a href=\"https:\/\/studysoup.com\/tsg\/1100886\/geometry-concepts-and-applications-student-edition-geometry-concepts-applic-1-edition-chapter-3-4-problem-3\">Use the terms adjacent angles, linear pair, or neither to describe angles 1 and 2 in as many ways as possible.<br><\/a>\u2022<a href=\"https:\/\/studysoup.com\/tsg\/1100905\/geometry-concepts-and-applications-student-edition-geometry-concepts-applic-1-edition-chapter-3-4-problem-22\">How many pairs of adjacent angles are in the design of the window shown at the right? Name them.<\/a><br>\u2022<a href=\"https:\/\/studysoup.com\/tsg\/1100916\/geometry-concepts-and-applications-student-edition-geometry-concepts-applic-1-edition-chapter-3-5-problem-1\">Draw a pair of adjacent angles that are complementary and have the same measure. What is the measure of each angle?<br><\/a>\u2022<a href=\"https:\/\/studysoup.com\/tsg\/1102349\/geometry-concepts-and-applications-student-edition-geometry-concepts-applic-1-edition-chapter-8-2-problem-29\">If the measure of one angle of a parallelogram increases, what happens to the measure of its adjacent angles so that the figure remains a parallelogram?<\/a><br><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Adjacent angles are two angles which share a common side while also having a common vertex without overlapping. If there is a lack of one of these properties, it is simply not an adjacent angle. In simple terms, they are two angles that are beside each other. Let&#8217;s break down the common terms we use [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":5755,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[5,6,8],"class_list":["post-5584","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math","tag-adjacent-angles","tag-common-side","tag-vertex"],"_links":{"self":[{"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/posts\/5584","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5584"}],"version-history":[{"count":0,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/wp\/v2\/posts\/5584\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=\/"}],"wp:attachment":[{"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5584"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5584"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/newblog.studysoup.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}