Supplementary Angle Definition<\/h2>\n
Supplementary Angle form 180\u00ba by adding two angles.<\/p>\n
![\"Supplementary](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/Supplementary-Angles.jpg\")
<\/p>\n
From the given figure, Angle AOC is one angle and angle BOC is another angle. By adding the two angles AOC and BOC, we get 180\u00ba. \u2220AOC and \u2220BOC are Supplementary Angles.
\n\u2220AOC + \u2220BOC = 180\u00b0<\/p>\n
Properties of Supplementary Angles<\/h3>\n
Have a look at the important properties of supplementary angles explained in the below modules. They are as such<\/p>\n
- \n
- The two angles are said to be supplementary angles when they add up to form 180\u00b0.<\/li>\n
- The two supplementary angles together make a straight line, but the angles need not be together.<\/li>\n
- Two acute angles cannot be a supplement by each other.<\/li>\n
- \u201cS\u201d of supplementary angles stands for the \u201cStraight\u201d line. This means they form 180\u00b0.<\/li>\n
- The two right angles are always supplementary.<\/li>\n<\/ul>\n
Adjacent and Non-Adjacent Supplementary Angles<\/h3>\n
The supplementary angles may be classified as either adjacent or non-adjacent. The adjacent supplementary angles have the common line segment or arm with each other. Also, the non-adjacent supplementary angles do not have the line segment or arm.<\/p>\n
![\"Supplementary-angles-non-adjacent\"](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/Supplementary-angles-non-adjacent-300x237.jpg\")
<\/p>\nSupplementary Angles Theorem<\/h3>\n
The supplementary angle theorem states that if two angles are supplementary to the same angle, then the two angles are said to be congruent.<\/p>\n
Proof:<\/p>\n
If \u2220a and \u2220b are two different angles that are supplementary to a third angle \u2220c, such that,
\n\u2220a + \u2220c = 180 \u2026\u2026. (1)
\n\u2220b + \u2220c = 180 \u2026\u2026. (2)
\nThen, from the above two equations, we can say,
\n\u2220a = \u2220b<\/p>\nHence proved.<\/p>\n
Supplementary Angles Examples<\/h3>\n
1. Verify if 125\u00b0, 55\u00b0 are a pair of supplementary angles?<\/p>\n
Solution:
\nAdd the given two angles and check if the resultant angle is 180\u00b0 or not.
\n125\u00b0 + 55\u00b0 = 180\u00b0<\/p>\nThe resultant angle is 180\u00b0. Hence, they are a pair of supplementary angles.<\/p>\n
2. Find the supplement of the angle (30 + x)\u00b0.<\/p>\n
Solution:
\nTo find the supplement of (30 + x)\u00b0, subtract it from 180\u00b0
\nSupplement of the angle (30 + x)\u00b0 = 180\u00b0 – (30 + x)\u00b0
\n= 180\u00b0 – 30\u00b0 – x\u00b0
\n= (150 – x) \u00b0<\/p>\n3. If angles of measures (y – 2)\u00b0 and (3y + 7)\u00b0 are a pair of supplementary angles. Find the measures.<\/p>\n
Solution:
\nSince (y – 2)\u00b0 and (3y + 7)\u00b0 represent a pair of supplementary angles, then their sum must be equal to 180\u00b0.
\nTherefore, (y – 2) + (3y + 7) = 180
\ny – 2 + 3y + 7 = 180
\ny + 3y – 2 + 7 = 180
\n4y + 5 = 180
\nSubtract 5 from both sides
\n4y + 5 – 5 = 180 – 5
\n4y = 180 – 5
\n4y = 175
\ny = 175\/4
\ny = 43.75\u00b0<\/p>\nTherefore, we know the value of y = 43.75\u00b0, put the value in place of y
\ny – 2
\n= 43.75 – 2
\n= 41.75\u00b0<\/p>\nAnd again, 3y + 7
\n= 3 \u00d7 43.75\u00b0 + 7
\n= 118 + 5
\n= 138.25\u00b0
\nTherefore, the two supplementary angles are 41.75\u00b0 and 138.25\u00b0.<\/p>\n4. Two supplementary angles are in the ratio 5 : 4. Find the measure of the angles.<\/p>\n
Solution:
\nLet the common ratio be m.
\nIf one angle is 5m, then the other angle is 4m.
\nTherefore, 5m + 4m = 180
\n9m = 180
\nm = 180\/9
\nm = 20
\nPut the value of m = 20<\/p>\nOne angle is 5m
\n= 5 \u00d7 20
\n= 100\u00b0<\/p>\nAnd the other angle is 4m
\n= 4 \u00d7 20
\n= 80\u00b0<\/p>\nTherefore, the two supplementary angles are 100\u00b0 and 80\u00b0.<\/p>\n
5. In the given figure find the measure of the unknown angle.<\/p>\n
![\"supplementary](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/01\/supplementary-angles-2.jpg\")
<\/p>\nSolution:
\nx + 45\u00b0 + 25\u00b0 = 180\u00b0
\nThe sum of angles at a point on a line on one side of it is 180\u00b0
\nTherefore, x + 70\u00b0 = 180\u00b0
\nSubtract 70\u00b0 from both sides
\nx + 70\u00b0 – 70\u00b0 = 180\u00b0 – 70\u00b0
\nx = 110\u00b0<\/p>\n","protected":false},"excerpt":{"rendered":"Supplementary angles are the angles that are added up to 180 degrees. If one angle is 120 degrees then the other angle is 60 degrees in supplementary angles because by adding 120 and 60, we get 180 degrees. By adding two supplementary angles, they form a straight line and a straight angle. One important thing … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35464"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=35464"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35464\/revisions"}],"predecessor-version":[{"id":92639,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35464\/revisions\/92639"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=35464"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=35464"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=35464"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}