![\"Pairs](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/pairs-of-angles-1.jpg\")
<\/p>\nAngles are formed when two lines intersect each other at a point. The pair of angles are nothing but two angles. The angle pairs can relate to each other in various ways. Those are complementary angles, supplementary angles, vertical angles, adjacent angles, alternate interior angles, alternate exterior angles, and corresponding angles.<\/p>\n
The region between two infinitely long lines pointing a certain direction from a common vertex is called an angle. Which is the amount of turn is measured by an angle. The pairs of angles mean two angles. If there is one common line for two angles, it is known as angle pairs. Get the definitions and examples of all pairs of angles in the following section.<\/p>\n
Two angles whose sum is 90\u00b0 are called complementary angles and one angle is the complement of another angle.<\/p>\n
<\/p>\n
Here, \u2220AOB = 20\u00b0, \u2220BOC = 70\u00b0<\/p>\n
So, \u2220AOB + \u2220BOC = 20\u00b0 + 70\u00b0 = 90\u00b0<\/p>\n
Therefore, \u2220AOB and \u2220BOC are called complementary angles.<\/p>\n
\u2220AOB is a complement of \u2220BOC and \u2220BOC is the complement of \u2220AOB.<\/p>\n
Example:<\/strong><\/p>\n (i) Angles of measure 50\u00b0 and 40\u00b0 are complementary angles because 50\u00b0 + 40\u00b0 = 90\u00b0.<\/p>\n Thus, the complementary angle of 50\u00b0 is the angle measure 40\u00b0. The complementary angle of 40\u00b0 is the angle measure 50\u00b0.<\/p>\n (ii) Complementary of 60\u00b0 is 90\u00b0 – 60\u00b0 = 30\u00b0<\/p>\n (iii) Complementary of 45\u00b0 is 90\u00b0 – 45\u00b0= 45\u00b0<\/p>\n (vi) Complementary of 25\u00b0 is 90 – 25\u00b0 = 65\u00b0<\/p>\n Working rule<\/strong>: To find the complementary angle of a given angle subtracts the measure of an angle from 90\u00b0.<\/p>\n So, the complementary angle = 90\u00b0 – given angle<\/p>\n Also, Read:<\/p>\n The pair of angles whose sum is 180\u00b0 is called the supplementary angles and one angle is called the supplement of the other angle.<\/p>\n Here, \u2220AOC = 120\u00b0, \u2220COB = 60\u00b0<\/p>\n \u2220AOC + \u2220COB = 120\u00b0 + 60\u00b0 = 180\u00b0<\/p>\n Therefore, \u2220AOC, \u2220COB are called supplementary angles.<\/p>\n \u2220AOC is the supplement of \u2220COB, \u2220COB is a supplement of \u2220AOC.<\/p>\n Example:<\/strong><\/p>\n (i) Angles of measure 90\u00b0 and 90\u00b0 are supplementary angles because 90\u00b0+ 90\u00b0 = 180\u00b0<\/p>\n Thus, the supplementary angle of 90\u00b0 is the angle of measure 90\u00b0.<\/p>\n (ii) Supplement of 100\u00b0 is 180\u00b0 – 100\u00b0 = 80\u00b0<\/p>\n (iii) Supplement of 50\u00b0 is 180\u00b0 – 50\u00b0 = 130\u00b0<\/p>\n (iv) Supplement of 95\u00b0 is 180\u00b0 – 95\u00b0= 85\u00b0<\/p>\n (v) Supplement of 140\u00b0 is 180\u00b0- 140\u00b0 = 40\u00b0<\/p>\n Working rule<\/strong>: To find the supplementary angle of the given angle, subtract the measure of angle from 180\u00b0.<\/p>\n So, the supplementary angle = 180\u00b0 – given angle<\/p>\n Two non-overlapping angles are said to be adjacent angles if they have a common vertex, common arm, and other two arms lying on the opposite side of this common arm so that their interiors do not overlap.<\/p>\n In the above figure, \u2220DBC and \u2220CBA are non-overlapping, have BC as the common arm and B as the common vertex. The other arms BD, AB of the angles \u2220DBC and \u2220CBA are opposite sides of the common arm BC.<\/p>\n Hence, the arm \u2220DBC and \u2220CBA form a pair of adjacent angles.<\/p>\n The angles are called liner pairs of angles when they are adjacent to each other after the intersection of two lines. Two adjacent angles are said to form a linear pair if their sum is 180\u00b0. The types of linear pairs of angles are alternate exterior angles, alternate interior angles, and corresponding angles.<\/p>\n Alternate interior angles<\/strong><\/p>\n Two angles in the interior of the parallel lines and on opposite sides of the transversal. Alternate interior angles are non-adjacent and congruent.<\/p>\n Alternate exterior angles<\/strong><\/p>\n Two angles in the exterior of the parallel lines, and on the opposite sides of the transversal. Alternate exterior angles are non-adjacent and congruent.<\/p>\n Corresponding angles<\/strong><\/p>\n The pair of angles, one in the interior and another in the exterior that is on the same side of the transversal. Corresponding angles are non-adjacent and congruent.<\/p>\n Two angles formed by two intersecting lines having no common arm are called the vertically opposite angles.<\/p>\n When two lines intersect, then vertically opposite angles are always equal.<\/p>\n \u22201 = \u22203<\/p>\n \u22202 = \u22204<\/p>\n Example 1:<\/strong><\/p>\n Suppose two angles \u2220AOC and \u2220 BOC form a linear pair at point O in a line segment AB. If the difference between the two angles is 40\u00b0. Then find both the angles.<\/p>\n Solution:<\/strong><\/p>\n Given that,<\/p>\n \u2220AOC and \u2220BOC form a linear pair<\/p>\n so, \u2220AOC + \u2220BOC = 180\u00b0 —- (i)<\/p>\n \u2220AOC – \u2220BOC = 40\u00b0 —- (ii)<\/p>\n Add both equations<\/p>\n \u2220AOC + \u2220BOC + \u2220AOC – \u2220BOC = 180\u00b0 + 40\u00b0<\/p>\n 2\u2220AOC = 220\u00b0<\/p>\n \u2220AOC = 220\u00b0 \/ 2<\/p>\n \u2220AOC = 110\u00b0<\/p>\n Now, substitute \u2220AOC in (i)<\/p>\n 110\u00b0 + \u2220 BOC = 180\u00b0<\/p>\n \u2220BOC = 180\u00b0 – 110\u00b0<\/p>\n \u2220BOC = 70\u00b0<\/p>\n Therefore, two angles are 70\u00b0, 110\u00b0.<\/p>\n Example 2:<\/strong><\/p>\n Find the values of the angles x, y, and z in the following figure.<\/p>\n Solution:<\/strong><\/p>\n From the given figure,<\/p>\n lines AD and EC intersect each other and \u2220DOC and \u2220AOE are vertically opposite angles<\/p>\n When two lines intersect, then vertically opposite angles are always equal.<\/p>\n So, \u2220DOC = \u2220AOE<\/p>\n Therefore, z = 40\u00b0<\/p>\n AD is a line<\/p>\n \u2220DOE and \u2220AOE are adjacent angles. The sum of adjacent angles are 180\u00b0<\/p>\n So, \u2220DOE + \u2220AOE = 180\u00b0<\/p>\n y + 40\u00b0 = 180\u00b0<\/p>\n y = 180\u00b0- 40\u00b0<\/p>\n y = 140\u00b0<\/p>\n And, lines AD and CE intersect<\/p>\n \u2220DOE, \u2220COA are vertically opposite.<\/p>\n When two lines intersect, then vertically opposite angles are always equal.<\/p>\n So, \u2220DOE = \u2220COA<\/p>\n y = \u2220COB + \u2220BOAA<\/p>\n 140\u00b0 = x + 25\u00b0<\/p>\n 140\u00b0 – 25\u00b0 = x<\/p>\n x = 115\u00b0<\/p>\n Hence, x = 115\u00b0, y = 140\u00b0, z = 40\u00b0<\/p>\n Example 3:<\/strong><\/p>\n Identify the five pairs of adjacent angles in the following figure.<\/p>\n Solution:<\/strong><\/p>\n Adjacent angles are the angles that have a common side, vertex, and no overlap.<\/p>\n So, (i) \u2220AOD, \u2220AOE are the adjacent angles<\/p>\n The common side is AO, the common vertex is O and OE, OD is not overlapping.<\/p>\n (ii) \u2220AOD, \u2220DOB is the adjacent angles<\/p>\n The common vertex is O, the common side is OD and OA, OB is not overlapping.<\/p>\n (iii) \u2220DOB, \u2220BOC is the adjacent angles<\/p>\n The common side is OB, the common vertex is O, and OD, OC are not overlapping.<\/p>\n (iv) \u2220COE, \u2220BOC are adjacent angles<\/p>\n The common side is OC, the common vertex is O, and OE, OB are not overlapping.<\/p>\n (v) \u2220COE, \u2220EOA are adjacent angles<\/p>\n The common vertex is O, the common side is OE, and OC, OA is not overlapping.<\/p>\n","protected":false},"excerpt":{"rendered":" Angles are formed when two lines intersect each other at a point. The pair of angles are nothing but two angles. The angle pairs can relate to each other in various ways. Those are complementary angles, supplementary angles, vertical angles, adjacent angles, alternate interior angles, alternate exterior angles, and corresponding angles. Pairs of Angles – … Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":52615,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Pairs-of-Angles.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/52245"}],"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\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=52245"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/52245\/revisions"}],"predecessor-version":[{"id":92501,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/52245\/revisions\/92501"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/52615"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=52245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=52245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=52245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
2. Supplementary Angles<\/h3>\n
![\"pairs](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/pairs-of-angles-3.jpg\")
<\/p>\n3. Adjacent Angles<\/h3>\n
![\"Pairs](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/pairs-of-angles-4.png\")
<\/p>\n4. Linear Pair of Angles<\/h3>\n
![\"pairs](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/pairs-of-angles-5.jpg\")
<\/p>\n![\"Pairs](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/pairs-of-angles-6.jpg\")
<\/p>\n![\"Pairs](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/pairs-of-angles-7.jpg\")
<\/p>\n5. Vertical Angles<\/h3>\n
![\"Pairs](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/pairs-of-angles-8.png\")
<\/p>\nPair of Angles Examples<\/h3>\n
![\"Pairs](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/pairs-of-angles-9.jpg\")
<\/p>\n![\"Pairs](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/pairs-of-angles-10.jpg\")
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