{"id":21639,"date":"2025-06-15T14:04:53","date_gmt":"2025-06-15T14:04:53","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=21639"},"modified":"2025-06-15T14:04:54","modified_gmt":"2025-06-15T14:04:54","slug":"angles-a-and-b-are-complementary","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/angles-a-and-b-are-complementary\/","title":{"rendered":"Angles A and B are complementary"},"content":{"rendered":"\n<p>Angles A and B are complementary. Two separate angles are shown. Angle A is (x + 22) degrees. Angle B is x degrees. What is the value of x? 34 56 68 79<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>Let&#8217;s analyze the problem step-by-step.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Problem Recap:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angles A and B are <strong>complementary<\/strong>.<\/li>\n\n\n\n<li>Angle A = x+22x + 22 degrees<\/li>\n\n\n\n<li>Angle B = xx degrees<\/li>\n\n\n\n<li>Find the value of xx.<\/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 1: Understand what &#8220;complementary&#8221; means<\/h3>\n\n\n\n<p>Two angles are <strong>complementary<\/strong> if their measures add up to <strong>90 degrees<\/strong>.<\/p>\n\n\n\n<p>Mathematically: A+B=90\u2218A + B = 90^\\circ<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Set up the equation<\/h3>\n\n\n\n<p>Given: A=x+22A = x + 22 B=xB = x<\/p>\n\n\n\n<p>Since they are complementary: (x+22)+x=90(x + 22) + x = 90<\/p>\n\n\n\n<p>Simplify: 2x+22=902x + 22 = 90<\/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 xx<\/h3>\n\n\n\n<p>Subtract 22 from both sides: 2x=90\u2212222x = 90 &#8211; 22 2x=682x = 68<\/p>\n\n\n\n<p>Divide both sides by 2: x=682=34x = \\frac{68}{2} = 34<\/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>34\\boxed{34}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation in detail:<\/h3>\n\n\n\n<p>Complementary angles always sum to 90 degrees. In this problem, you have two angles expressed in terms of xx, and since they add to 90 degrees, you can form an equation that represents this relationship.<\/p>\n\n\n\n<p>By substituting the expressions for angles A and B into the equation A+B=90A + B = 90, you get a linear equation in terms of xx. Simplifying this equation gives you 2x+22=902x + 22 = 90.<\/p>\n\n\n\n<p>You then isolate xx by subtracting 22 from both sides and dividing by 2, resulting in x=34x = 34.<\/p>\n\n\n\n<p>This means angle B measures 34 degrees, and angle A measures 34+22=5634 + 22 = 56 degrees. Together, 34+56=9034 + 56 = 90, confirming that they are complementary.<\/p>\n\n\n\n<p>Therefore, the value of xx is 34 degrees.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Angles A and B are complementary. Two separate angles are shown. Angle A is (x + 22) degrees. Angle B is x degrees. What is the value of x? 34 56 68 79 The correct answer and explanation is: Let&#8217;s analyze the problem step-by-step. Problem Recap: Step 1: Understand what &#8220;complementary&#8221; means Two angles are [&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-21639","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21639","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=21639"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21639\/revisions"}],"predecessor-version":[{"id":21641,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21639\/revisions\/21641"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=21639"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=21639"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=21639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}