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

2. Goals Vertical Angles and Linear Pairs Complementary and Supplementary Angles

3. 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 3 4 <1 & <2 are vertical. m<1 ≅ m< 2. <3 & <4 are vertical. m<3 ≅ m<4.

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°

5. 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°

6. 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°

7. 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? 1 2 3 4 5 Yes No, <4+<5≠180° No, <3≠<5 Yes

8. 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. 36 1 3 2

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

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

11. Answers to #3 1)4x + 15 + 5x + 30 = 180° 2)9x + 45 = 180° 3)9x = 135° 4)x = 15 X Y 1)3y + 15 + 3y - 15 = 180° 2)6y = 180° 3)y = 30

12. 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.

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

14. Assignment Page 47 #8-32 66-71