{"id":4438,"date":"2020-04-13T13:27:22","date_gmt":"2020-04-13T13:27:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4438"},"modified":"2021-02-06T00:04:23","modified_gmt":"2021-02-06T00:04:23","slug":"using-properties-of-angles-to-solve-problems","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/using-properties-of-angles-to-solve-problems\/","title":{"raw":"Using Properties of Angles to Solve Problems","rendered":"Using Properties of Angles to Solve Problems"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find the supplement of an angle<\/li>\r\n \t<li>Find the complement of an angle<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>Are you familiar with the phrase 'do a [latex]180[\/latex]?' It means to make a full turn so that you face the opposite direction. It comes from the fact that the measure of an angle that makes a straight line is [latex]180[\/latex] degrees. See the image below.<\/p>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223529\/CNX_BMath_Figure_09_03_046_img.png\" alt=\"The image is a straight line with an arrow on each end. There is a dot in the center. There is an arrow pointing from one side of the dot to the other, and the angle is marked as 180 degrees.\" \/>\r\nAn angle is formed by two rays that share a common endpoint. Each ray is called a side of the angle and the common endpoint is called the vertex. An angle is named by its vertex. In the image below, [latex]\\angle A[\/latex] is the angle with vertex at point [latex]A[\/latex]. The measure of [latex]\\angle A[\/latex] is written [latex]m\\angle A[\/latex].\r\n<div class=\"textbox shaded\">\r\n\r\n[latex]\\angle A[\/latex] is the angle with vertex at [latex]\\text{point }A[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223530\/CNX_BMath_Figure_09_03_001.png\" alt=\"The image is an angle made up of two rays. The angle is labeled with letter A.\" \/>\r\n\r\n<\/div>\r\nWe measure angles in degrees, and use the symbol [latex]^ \\circ[\/latex] to represent degrees. We use the abbreviation [latex]m[\/latex] to for the <em>measure<\/em> of an angle. So if [latex]\\angle A[\/latex] is [latex]\\text{27}^ \\circ [\/latex], we would write [latex]m\\angle A=27[\/latex].\r\n\r\nIf the sum of the measures of two angles is [latex]\\text{180}^ \\circ[\/latex], then they are called supplementary angles. In the images below, each pair of angles is supplementary because their measures add to [latex]\\text{180}^ \\circ [\/latex]. Each angle is the <em>supplement<\/em> of the other.\r\n\r\nThe sum of the measures of supplementary angles is [latex]\\text{180}^ \\circ [\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223532\/CNX_BMath_Figure_09_03_003.png\" alt=\"Part a shows a 120 degree angle next to a 60 degree angle. Together, the angles form a straight line. Below the image, it reads 120 degrees plus 60 degrees equals 180 degrees. Part b shows a 45 degree angle attached to a 135 degree angle. Together, the angles form a straight line. Below the image, it reads 45 degrees plus 135 degrees equals 180 degrees.\" \/>\r\nIf the sum of the measures of two angles is [latex]\\text{90}^ \\circ[\/latex], then the angles are complementary angles. In the images below, each pair of angles is complementary, because their measures add to [latex]\\text{90}^ \\circ[\/latex]. Each angle is the <em>complement<\/em> of the other.\r\n\r\nThe sum of the measures of complementary angles is [latex]\\text{90}^ \\circ[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223533\/CNX_BMath_Figure_09_03_004.png\" alt=\"Part a shows a 50 degree angle next to a 40 degree angle. Together, the angles form a right angle. Below the image, it reads 50 degrees plus 40 degrees equals 90 degrees. Part b shows a 60 degree angle attached to a 30 degree angle. Together, the angles form a right angle. Below the image, it reads 60 degrees plus 30 degrees equals 90 degrees.\" \/>\r\n<div class=\"textbox shaded\">\r\n<h3>Supplementary and Complementary Angles<\/h3>\r\nIf the sum of the measures of two angles is [latex]\\text{180}^\\circ [\/latex], then the angles are <strong>supplementary<\/strong>.\r\n<p style=\"padding-left: 60px\">If angle [latex]A[\/latex] and angle [latex]B[\/latex] are supplementary, then [latex]m\\angle{A}+m\\angle{B}=180^\\circ[\/latex].<\/p>\r\nIf the sum of the measures of two angles is [latex]\\text{90}^\\circ[\/latex], then the angles are <strong>complementary<\/strong>.\r\n<p style=\"padding-left: 60px\">If angle [latex]A[\/latex] and angle [latex]B[\/latex] are complementary, then [latex]m\\angle{A}+m\\angle{B}=90^\\circ[\/latex].<\/p>\r\n\r\n<\/div>\r\nIn this section and the next, you will be introduced to some common geometry formulas. We will adapt our Problem Solving Strategy for Geometry Applications. The geometry formula will name the variables and give us the equation to solve.\r\n\r\nIn addition, since these applications will all involve geometric shapes, it will be helpful to draw a figure and then label it with the information from the problem. We will include this step in the Problem Solving Strategy for Geometry Applications.\r\n<div class=\"textbox shaded\">\r\n<h3>Use a Problem Solving Strategy for Geometry Applications.<\/h3>\r\n<ol id=\"eip-id1170325410595\" class=\"stepwise\">\r\n \t<li><strong>Read<\/strong> the problem and make sure you understand all the words and ideas. Draw a figure and label it with the given information.<\/li>\r\n \t<li><strong>Identify<\/strong> what you are looking for.<\/li>\r\n \t<li><strong>Name<\/strong> what you are looking for and choose a variable to represent it.<\/li>\r\n \t<li><strong>Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\r\n \t<li><strong>Solve<\/strong> the equation using good algebra techniques.<\/li>\r\n \t<li><strong>Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\r\n \t<li><strong>Answer<\/strong> the question with a complete sentence.<\/li>\r\n<\/ol>\r\n<\/div>\r\nThe next example will show how you can use the Problem Solving Strategy for Geometry Applications to answer questions about supplementary and complementary angles.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAn angle measures [latex]\\text{40}^ \\circ[\/latex].\r\n\r\n1. Find its supplement\r\n\r\n2. Find its complement\r\n\r\nSolution\r\n<table id=\"eip-id1168469720851\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">1.<\/td>\r\n<td style=\"height: 15px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 101.875px\">\r\n<td style=\"height: 101.875px\">Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td style=\"height: 101.875px\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223535\/CNX_BMath_Figure_09_03_047_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td style=\"height: 15px\">The supplement of a [latex]40\u00b0[\/latex]angle.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td style=\"height: 15px\">Let [latex]s=[\/latex]the measure of the supplement.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 73px\">\r\n<td style=\"height: 73px\">Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula for the situation and substitute in the given information.<\/td>\r\n<td style=\"height: 73px\">[latex]m\\angle A+m\\angle B=180[\/latex]\r\n\r\n[latex]s+40=180[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td style=\"height: 15px\">[latex]s=140[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 88px\">\r\n<td style=\"height: 88px\">Step 6. <strong>Check:<\/strong>\r\n\r\n[latex]140+40\\stackrel{?}{=}180[\/latex]\r\n\r\n[latex]180=180\\checkmark[\/latex]<\/td>\r\n<td style=\"height: 88px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\">Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td style=\"height: 30px\">The supplement of the [latex]40\u00b0[\/latex]angle is [latex]140\u00b0[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468558393\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223548\/CNX_BMath_Figure_09_03_048_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>\r\n<table id=\"eip-id1168469720851\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">The complement of a [latex]40\u00b0[\/latex]angle.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let [latex]c=[\/latex]the measure of the complement.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula for the situation and substitute in the given information.<\/td>\r\n<td>[latex]m\\angle A+m\\angle B=90[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]c+40=90[\/latex]\r\n\r\n[latex]c=50[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\n[latex]50+40\\stackrel{?}{=}90[\/latex]\r\n\r\n[latex]90=90\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The complement of the [latex]40\u00b0[\/latex]angle is [latex]50\u00b0[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146495[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to find the supplement and complement of an angle.\r\n\r\nhttps:\/\/youtu.be\/ZQ_L3yJOfqM\r\n\r\nDid you notice that the words complementary and supplementary are in alphabetical order just like [latex]90[\/latex] and [latex]180[\/latex] are in numerical order?\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nTwo angles are supplementary. The larger angle is [latex]\\text{30}^ \\circ[\/latex] more than the smaller angle. Find the measure of both angles.\r\n\r\n[reveal-answer q=\"190834\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"190834\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468587362\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223601\/CNX_BMath_Figure_09_03_049_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>The measures of both angles.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.\r\n\r\nThe larger angle is 30\u00b0 more than the smaller angle.<\/td>\r\n<td>Let [latex]a=[\/latex] measure of smaller angle\r\n\r\n[latex]a+30=[\/latex] measure of larger angle<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula and substitute.<\/td>\r\n<td>[latex]m\\angle A+m\\angle B=180[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex](a+30)+a=180[\/latex]\r\n\r\n[latex]2a+30=180[\/latex]\r\n\r\n[latex]2a=150[\/latex]\r\n\r\n[latex]a=75=[\/latex] measure of smaller angle.\r\n\r\n[latex]a+30=[\/latex] measure of larger angle.\r\n\r\n[latex]75+30[\/latex]\r\n\r\n[latex]105[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\n[latex]m\\angle A+m\\angle B=180[\/latex]\r\n\r\n[latex]75+105\\stackrel{?}{=}180[\/latex]\r\n\r\n[latex]180=180\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The measures of the angle are [latex]75\u00b0[\/latex]and [latex]105\u00b0[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146496[\/ohm_question]\r\n\r\n[ohm_question]146497[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find the supplement of an angle<\/li>\n<li>Find the complement of an angle<\/li>\n<\/ul>\n<\/div>\n<p>Are you familiar with the phrase &#8216;do a [latex]180[\/latex]?&#8217; It means to make a full turn so that you face the opposite direction. It comes from the fact that the measure of an angle that makes a straight line is [latex]180[\/latex] degrees. See the image below.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223529\/CNX_BMath_Figure_09_03_046_img.png\" alt=\"The image is a straight line with an arrow on each end. There is a dot in the center. There is an arrow pointing from one side of the dot to the other, and the angle is marked as 180 degrees.\" \/><br \/>\nAn angle is formed by two rays that share a common endpoint. Each ray is called a side of the angle and the common endpoint is called the vertex. An angle is named by its vertex. In the image below, [latex]\\angle A[\/latex] is the angle with vertex at point [latex]A[\/latex]. The measure of [latex]\\angle A[\/latex] is written [latex]m\\angle A[\/latex].<\/p>\n<div class=\"textbox shaded\">\n<p>[latex]\\angle A[\/latex] is the angle with vertex at [latex]\\text{point }A[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223530\/CNX_BMath_Figure_09_03_001.png\" alt=\"The image is an angle made up of two rays. The angle is labeled with letter A.\" \/><\/p>\n<\/div>\n<p>We measure angles in degrees, and use the symbol [latex]^ \\circ[\/latex] to represent degrees. We use the abbreviation [latex]m[\/latex] to for the <em>measure<\/em> of an angle. So if [latex]\\angle A[\/latex] is [latex]\\text{27}^ \\circ[\/latex], we would write [latex]m\\angle A=27[\/latex].<\/p>\n<p>If the sum of the measures of two angles is [latex]\\text{180}^ \\circ[\/latex], then they are called supplementary angles. In the images below, each pair of angles is supplementary because their measures add to [latex]\\text{180}^ \\circ[\/latex]. Each angle is the <em>supplement<\/em> of the other.<\/p>\n<p>The sum of the measures of supplementary angles is [latex]\\text{180}^ \\circ[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223532\/CNX_BMath_Figure_09_03_003.png\" alt=\"Part a shows a 120 degree angle next to a 60 degree angle. Together, the angles form a straight line. Below the image, it reads 120 degrees plus 60 degrees equals 180 degrees. Part b shows a 45 degree angle attached to a 135 degree angle. Together, the angles form a straight line. Below the image, it reads 45 degrees plus 135 degrees equals 180 degrees.\" \/><br \/>\nIf the sum of the measures of two angles is [latex]\\text{90}^ \\circ[\/latex], then the angles are complementary angles. In the images below, each pair of angles is complementary, because their measures add to [latex]\\text{90}^ \\circ[\/latex]. Each angle is the <em>complement<\/em> of the other.<\/p>\n<p>The sum of the measures of complementary angles is [latex]\\text{90}^ \\circ[\/latex].<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223533\/CNX_BMath_Figure_09_03_004.png\" alt=\"Part a shows a 50 degree angle next to a 40 degree angle. Together, the angles form a right angle. Below the image, it reads 50 degrees plus 40 degrees equals 90 degrees. Part b shows a 60 degree angle attached to a 30 degree angle. Together, the angles form a right angle. Below the image, it reads 60 degrees plus 30 degrees equals 90 degrees.\" \/><\/p>\n<div class=\"textbox shaded\">\n<h3>Supplementary and Complementary Angles<\/h3>\n<p>If the sum of the measures of two angles is [latex]\\text{180}^\\circ[\/latex], then the angles are <strong>supplementary<\/strong>.<\/p>\n<p style=\"padding-left: 60px\">If angle [latex]A[\/latex] and angle [latex]B[\/latex] are supplementary, then [latex]m\\angle{A}+m\\angle{B}=180^\\circ[\/latex].<\/p>\n<p>If the sum of the measures of two angles is [latex]\\text{90}^\\circ[\/latex], then the angles are <strong>complementary<\/strong>.<\/p>\n<p style=\"padding-left: 60px\">If angle [latex]A[\/latex] and angle [latex]B[\/latex] are complementary, then [latex]m\\angle{A}+m\\angle{B}=90^\\circ[\/latex].<\/p>\n<\/div>\n<p>In this section and the next, you will be introduced to some common geometry formulas. We will adapt our Problem Solving Strategy for Geometry Applications. The geometry formula will name the variables and give us the equation to solve.<\/p>\n<p>In addition, since these applications will all involve geometric shapes, it will be helpful to draw a figure and then label it with the information from the problem. We will include this step in the Problem Solving Strategy for Geometry Applications.<\/p>\n<div class=\"textbox shaded\">\n<h3>Use a Problem Solving Strategy for Geometry Applications.<\/h3>\n<ol id=\"eip-id1170325410595\" class=\"stepwise\">\n<li><strong>Read<\/strong> the problem and make sure you understand all the words and ideas. Draw a figure and label it with the given information.<\/li>\n<li><strong>Identify<\/strong> what you are looking for.<\/li>\n<li><strong>Name<\/strong> what you are looking for and choose a variable to represent it.<\/li>\n<li><strong>Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n<li><strong>Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong>Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong>Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<p>The next example will show how you can use the Problem Solving Strategy for Geometry Applications to answer questions about supplementary and complementary angles.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>An angle measures [latex]\\text{40}^ \\circ[\/latex].<\/p>\n<p>1. Find its supplement<\/p>\n<p>2. Find its complement<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168469720851\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">1.<\/td>\n<td style=\"height: 15px\"><\/td>\n<\/tr>\n<tr style=\"height: 101.875px\">\n<td style=\"height: 101.875px\">Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td style=\"height: 101.875px\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223535\/CNX_BMath_Figure_09_03_047_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td style=\"height: 15px\">The supplement of a [latex]40\u00b0[\/latex]angle.<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td style=\"height: 15px\">Let [latex]s=[\/latex]the measure of the supplement.<\/td>\n<\/tr>\n<tr style=\"height: 73px\">\n<td style=\"height: 73px\">Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula for the situation and substitute in the given information.<\/td>\n<td style=\"height: 73px\">[latex]m\\angle A+m\\angle B=180[\/latex]<\/p>\n<p>[latex]s+40=180[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td style=\"height: 15px\">[latex]s=140[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 88px\">\n<td style=\"height: 88px\">Step 6. <strong>Check:<\/strong><\/p>\n<p>[latex]140+40\\stackrel{?}{=}180[\/latex]<\/p>\n<p>[latex]180=180\\checkmark[\/latex]<\/td>\n<td style=\"height: 88px\"><\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\">Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td style=\"height: 30px\">The supplement of the [latex]40\u00b0[\/latex]angle is [latex]140\u00b0[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468558393\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223548\/CNX_BMath_Figure_09_03_048_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>\n<table id=\"eip-id1168469720851\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">The complement of a [latex]40\u00b0[\/latex]angle.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let [latex]c=[\/latex]the measure of the complement.<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula for the situation and substitute in the given information.<\/td>\n<td>[latex]m\\angle A+m\\angle B=90[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]c+40=90[\/latex]<\/p>\n<p>[latex]c=50[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>[latex]50+40\\stackrel{?}{=}90[\/latex]<\/p>\n<p>[latex]90=90\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The complement of the [latex]40\u00b0[\/latex]angle is [latex]50\u00b0[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146495\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146495&theme=oea&iframe_resize_id=ohm146495&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to find the supplement and complement of an angle.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Determine the Complement and Supplement of a Given Angle\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ZQ_L3yJOfqM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Did you notice that the words complementary and supplementary are in alphabetical order just like [latex]90[\/latex] and [latex]180[\/latex] are in numerical order?<\/p>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Two angles are supplementary. The larger angle is [latex]\\text{30}^ \\circ[\/latex] more than the smaller angle. Find the measure of both angles.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q190834\">Show Solution<\/span><\/p>\n<div id=\"q190834\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468587362\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223601\/CNX_BMath_Figure_09_03_049_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>The measures of both angles.<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/p>\n<p>The larger angle is 30\u00b0 more than the smaller angle.<\/td>\n<td>Let [latex]a=[\/latex] measure of smaller angle<\/p>\n<p>[latex]a+30=[\/latex] measure of larger angle<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula and substitute.<\/td>\n<td>[latex]m\\angle A+m\\angle B=180[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex](a+30)+a=180[\/latex]<\/p>\n<p>[latex]2a+30=180[\/latex]<\/p>\n<p>[latex]2a=150[\/latex]<\/p>\n<p>[latex]a=75=[\/latex] measure of smaller angle.<\/p>\n<p>[latex]a+30=[\/latex] measure of larger angle.<\/p>\n<p>[latex]75+30[\/latex]<\/p>\n<p>[latex]105[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>[latex]m\\angle A+m\\angle B=180[\/latex]<\/p>\n<p>[latex]75+105\\stackrel{?}{=}180[\/latex]<\/p>\n<p>[latex]180=180\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The measures of the angle are [latex]75\u00b0[\/latex]and [latex]105\u00b0[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146496\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146496&theme=oea&iframe_resize_id=ohm146496&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146497\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146497&theme=oea&iframe_resize_id=ohm146497&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4438\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146497, 146496, 146495. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Determine the Complement and Supplement of a Given Angle. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/ZQ_L3yJOfqM\">https:\/\/youtu.be\/ZQ_L3yJOfqM<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146497, 146496, 146495\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Determine the Complement and Supplement of a Given Angle\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/ZQ_L3yJOfqM\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4438","chapter","type-chapter","status-web-only","hentry"],"part":3706,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4438","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4438\/revisions"}],"predecessor-version":[{"id":4439,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4438\/revisions\/4439"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/3706"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4438\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4438"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4438"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4438"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}