{"id":21084,"date":"2025-06-15T07:23:31","date_gmt":"2025-06-15T07:23:31","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=21084"},"modified":"2025-06-15T07:23:42","modified_gmt":"2025-06-15T07:23:42","slug":"the-measure-of-angle-jkl-can-be-represented-using-the-expression-3x-5","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-measure-of-angle-jkl-can-be-represented-using-the-expression-3x-5\/","title":{"rendered":"The measure of angle JKL can be represented using the expression 3x + 5"},"content":{"rendered":"\n<p>The measure of angle JKL can be represented using the expression 3x + 5. Point K has three lines extending from it. One line extends to point J, another to point M, and the other to point L. Angle J K M is 45 degrees. Angle M K L is x degrees. What is the degree measure of Angle JKL? \u00b0<\/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 break down 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\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Point <strong>K<\/strong> has three lines extending to points <strong>J<\/strong>, <strong>M<\/strong>, and <strong>L<\/strong>.<\/li>\n\n\n\n<li>Angle <strong>JKL<\/strong> is represented by the expression 3x+53x + 5.<\/li>\n\n\n\n<li>Angle <strong>JKM<\/strong> measures 45\u221845^\\circ.<\/li>\n\n\n\n<li>Angle <strong>MKL<\/strong> measures x\u2218x^\\circ.<\/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\">Goal:<\/h3>\n\n\n\n<p>Find the degree measure of angle <strong>JKL<\/strong>.<\/p>\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 the angles around point K<\/h3>\n\n\n\n<p>The three lines from point K to points J, M, and L create three adjacent angles around K:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angle JKM=45\u2218JKM = 45^\\circ<\/li>\n\n\n\n<li>Angle MKL=x\u2218MKL = x^\\circ<\/li>\n\n\n\n<li>Angle JKL=3x+5JKL = 3x + 5 (this is the angle between line KJ and KL)<\/li>\n<\/ul>\n\n\n\n<p>From the naming of the angles, it appears the three angles around K formed between the rays KJ, KM, and KL are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220JKM=45\u2218\\angle JKM = 45^\\circ<\/li>\n\n\n\n<li>\u2220MKL=x\u2218\\angle MKL = x^\\circ<\/li>\n\n\n\n<li>\u2220JKL=?\\angle JKL = ? (but the problem states it equals 3x+53x + 5)<\/li>\n<\/ul>\n\n\n\n<p>However, note that <strong>JKL<\/strong> is an angle formed between points J-K-L. It appears that \u2220JKL\\angle JKL is the sum of \u2220JKM\\angle JKM and \u2220MKL\\angle MKL, i.e.: \u2220JKL=\u2220JKM+\u2220MKL\\angle JKL = \\angle JKM + \\angle MKL<\/p>\n\n\n\n<p>So, 3x+5=45+x3x + 5 = 45 + x<\/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: Solve the equation<\/h3>\n\n\n\n<p>3x+5=45+x3x + 5 = 45 + x<\/p>\n\n\n\n<p>Subtract xx from both sides: 3x\u2212x+5=453x &#8211; x + 5 = 45 2x+5=452x + 5 = 45<\/p>\n\n\n\n<p>Subtract 5 from both sides: 2x=402x = 40<\/p>\n\n\n\n<p>Divide both sides by 2: x=20x = 20<\/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: Calculate angle JKLJKL<\/h3>\n\n\n\n<p>Recall, \u2220JKL=3x+5=3(20)+5=60+5=65\u2218\\angle JKL = 3x + 5 = 3(20) + 5 = 60 + 5 = 65^\\circ<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final answer:<\/strong><\/h3>\n\n\n\n<p>65\u2218\\boxed{65^\\circ}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>In this problem, point K is the vertex where three rays or lines extend to points J, M, and L. The angles formed at K are adjacent, and the sum of the smaller angles \u2220JKM\\angle JKM and \u2220MKL\\angle MKL equals the larger angle \u2220JKL\\angle JKL, which is represented algebraically as 3x+53x + 5.<\/p>\n\n\n\n<p>By setting up the equation 3x+5=45+x3x + 5 = 45 + x, we find the value of xx, which is the unknown angle measure of \u2220MKL\\angle MKL. Once xx is found, substituting it back into the expression for \u2220JKL\\angle JKL gives us the degree measure of \u2220JKL\\angle JKL.<\/p>\n\n\n\n<p>Thus, the angle \u2220JKL\\angle JKL measures <strong>65 degrees<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The measure of angle JKL can be represented using the expression 3x + 5. Point K has three lines extending from it. One line extends to point J, another to point M, and the other to point L. Angle J K M is 45 degrees. Angle M K L is x degrees. What is the [&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-21084","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21084","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=21084"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21084\/revisions"}],"predecessor-version":[{"id":21085,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21084\/revisions\/21085"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=21084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=21084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=21084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}