Section 1.6 Angle Pair Relationships standard #13 7/3/2016

Goals Vertical Angles and Linear Pairs Complementary and Supplementary Angles

Vertical Angles 2 angles whose sides form two pairs of opposite rays. These angles are congruent and lie on opposite sides of the point of intersection <1 & <2 are vertical. m<1 ≅ m< 2. <3 & <4 are vertical. m<3 ≅ m<4.

Linear Pair Two adjacent angles whose non-common sides are opposite rays. The angles will add up to 180°. The angles lie on the same line. 1 2 m<1 + m<2 = 180°

Complementary Angles Two angles that add to 90°. Each angle is the complement of the other. However, these angles do not have to be adjacent in order to be complementary. 1 2m<1 + m<2 = 90°

Supplementary Angles Two angles that add to 180°. Each angle is the supplement of the other. However, these angles do not have to be adjacent in order to be supplementary. 1 2 m<1 + m<2 = 180°

Example #1 A. Are  1 and  2 a linear pair? B. Are  4 and  5 a linear pair? C. Are  5 and  3 vertical angles? D. Are  1 and  3 vertical angles? Yes No, <4+<5≠180° No, <3≠<5 Yes

Example #2 In one town, Main Street and Columbus Avenue intersect to form an angle of 36°. Find the measures of the other three angles

Answers to #2 36° ) m<1 = 144° (180-36) 2) m<2 = 36° (Vertical Angles are congruent) 3) m<3 = 144° (Vertical Angles are congruent)

Example #3 Solve for x and y. Then find the angle measures. 4x+15 5x+30 3y-15 3y+15

Answers to #3 1)4x x + 30 = 180° 2)9x + 45 = 180° 3)9x = 135° 4)x = 15 X Y 1)3y y - 15 = 180° 2)6y = 180° 3)y = 30

Example #4 A.Given that  G is a supplement of  H and m  G is 82°, find m  H. B. Given that  U is a complement of  V, and m  U is 73°, find m  V.

Answers to #4 1)82° + m  H = 180° 2) m  H = 98° 1)73° + m  V = 90° 2) m  V = 17°

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