{"id":30870,"date":"2025-06-21T20:28:42","date_gmt":"2025-06-21T20:28:42","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=30870"},"modified":"2025-06-21T20:28:44","modified_gmt":"2025-06-21T20:28:44","slug":"regents-exam-questions-g-co-c-11-trapezoids-1a-www-jmap-org-10","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/regents-exam-questions-g-co-c-11-trapezoids-1a-www-jmap-org-10\/","title":{"rendered":"Regents Exam Questions G.CO.C.11: Trapezoids 1a www.jmap.org 10"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">Regents Exam Questions G.CO.C.11: Trapezoids 1a www.jmap.org 10<\/pre>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-162-1024x768.png\" alt=\"\" class=\"wp-image-30876\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-162-1024x768.png 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-162-300x225.png 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-162-768x576.png 768w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-162-1536x1152.png 1536w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-162-2048x1536.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given a trapezoid ABCDABCDABCD, where AB\u203e\\overline{AB}AB and CD\u203e\\overline{CD}CD are the bases. The angles provided are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220B=123\u2218\\angle B = 123^\\circ\u2220B=123\u2218<\/li>\n\n\n\n<li>\u2220D=75\u2218\\angle D = 75^\\circ\u2220D=75\u2218<\/li>\n<\/ul>\n\n\n\n<p>We are asked to find m\u2220Cm\\angle Cm\u2220C.<\/p>\n\n\n\n<p>In any quadrilateral, the sum of the interior angles is always 360 degrees. So:m\u2220A+m\u2220B+m\u2220C+m\u2220D=360\u2218m\\angle A + m\\angle B + m\\angle C + m\\angle D = 360^\\circm\u2220A+m\u2220B+m\u2220C+m\u2220D=360\u2218<\/p>\n\n\n\n<p>We are given:m\u2220B=123\u2218,m\u2220D=75\u2218m\\angle B = 123^\\circ,\\quad m\\angle D = 75^\\circm\u2220B=123\u2218,m\u2220D=75\u2218<\/p>\n\n\n\n<p>Let\u2019s substitute into the equation:m\u2220A+123+m\u2220C+75=360m\\angle A + 123 + m\\angle C + 75 = 360m\u2220A+123+m\u2220C+75=360<\/p>\n\n\n\n<p>Simplify:m\u2220A+m\u2220C=360\u2212(123+75)=162\u2218m\\angle A + m\\angle C = 360 &#8211; (123 + 75) = 162^\\circm\u2220A+m\u2220C=360\u2212(123+75)=162\u2218<\/p>\n\n\n\n<p>Since ABABAB and CDCDCD are the bases, angles AAA and DDD are same-side interior angles, and BBB and CCC are same-side interior angles. In trapezoids, same-side interior angles between the bases are supplementary. That means:m\u2220B+m\u2220C=180\u2218m\\angle B + m\\angle C = 180^\\circm\u2220B+m\u2220C=180\u2218<\/p>\n\n\n\n<p>We already know:m\u2220B=123\u2218m\\angle B = 123^\\circm\u2220B=123\u2218<\/p>\n\n\n\n<p>So:123+m\u2220C=180\u21d2m\u2220C=57\u2218123 + m\\angle C = 180 \\Rightarrow m\\angle C = 57^\\circ123+m\u2220C=180\u21d2m\u2220C=57\u2218<\/p>\n\n\n\n<p><strong>Final Answer: 1) 57<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>In a trapezoid, two of the sides are parallel. These parallel sides form what are known as base angles. A special property of trapezoids is that any pair of consecutive angles between a leg and the parallel bases are supplementary. This means their measures add up to 180 degrees. In trapezoid ABCDABCDABCD, sides AB\u203e\\overline{AB}AB and CD\u203e\\overline{CD}CD are given as the bases. Therefore, angles BBB and CCC lie between the same leg and these parallel sides, which makes them consecutive interior angles. That means they are supplementary.<\/p>\n\n\n\n<p>We are given that angle BBB measures 123 degrees. To find angle CCC, we use the supplementary angle rule:m\u2220B+m\u2220C=180\u2218\u21d2123+m\u2220C=180\u21d2m\u2220C=180\u2212123=57\u2218m\\angle B + m\\angle C = 180^\\circ \\Rightarrow 123 + m\\angle C = 180 \\Rightarrow m\\angle C = 180 &#8211; 123 = 57^\\circm\u2220B+m\u2220C=180\u2218\u21d2123+m\u2220C=180\u21d2m\u2220C=180\u2212123=57\u2218<\/p>\n\n\n\n<p>We can also verify this by adding up all the interior angles of the quadrilateral. All four interior angles of any quadrilateral add up to 360 degrees. Knowing angle B=123\u2218B = 123^\\circB=123\u2218 and angle D=75\u2218D = 75^\\circD=75\u2218, we can find the sum of the remaining two angles AAA and CCC as:m\u2220A+m\u2220C=360\u2212(123+75)=162\u2218m\\angle A + m\\angle C = 360 &#8211; (123 + 75) = 162^\\circm\u2220A+m\u2220C=360\u2212(123+75)=162\u2218<\/p>\n\n\n\n<p>This confirms our result again, since angle A=105\u2218A = 105^\\circA=105\u2218 and angle C=57\u2218C = 57^\\circC=57\u2218 would satisfy this. Therefore, the correct measure of angle CCC is 57 degrees.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-217.jpeg\" alt=\"\" class=\"wp-image-30877\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-217.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-217-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Regents Exam Questions G.CO.C.11: Trapezoids 1a www.jmap.org 10 The Correct Answer and Explanation is: We are given a trapezoid ABCDABCDABCD, where AB\u203e\\overline{AB}AB and CD\u203e\\overline{CD}CD are the bases. The angles provided are: We are asked to find m\u2220Cm\\angle Cm\u2220C. In any quadrilateral, the sum of the interior angles is always 360 degrees. So:m\u2220A+m\u2220B+m\u2220C+m\u2220D=360\u2218m\\angle A + m\\angle [&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-30870","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/30870","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=30870"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/30870\/revisions"}],"predecessor-version":[{"id":30878,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/30870\/revisions\/30878"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=30870"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=30870"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=30870"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}