1. 1.6 Angle Pair Relationships

2. Which angles are adjacent? 1 3 2 4 <1&<2, <2&<3, <3&<4, <4&<1 Vertical Angles – 2 angles that share a common vertex & whose sides form 2 pairs of opposite rays. <1&<3, <2&<4 Then what do we call <1&<3?

3. Linear Pair (of angles) 2 adjacent angles whose non-common sides are opposite rays. 1 2

4. Example Vertical angles? <1 & <4 Adjacent angles? <1&<2, <2&<3, <3&<4, <4&<5, <5&<1 Linear pair? <5&<4, <1&<5 Adjacent angles not a linear pair? <1&<2, <2&<3, <3&<4 1 3 2 5 4

5. Important Facts Vertical Angles are congruent. The sum of the measures of the angles in a linear pair is 180 o.

6. Example: If m<5=130 o, find m<3 m<6 m<4 5 3 4 6 =130 o =50 o

7. Example: Find x y m<ABE m<ABD m<DBC m<EBC 3x+5 o y+20 o x+15 o 4y-15 o x=40 y=35 m<ABE=125 o m<ABD=55 o m<DBC=125 o m<EBC=55 o A B C D E

8. Complementary Angles 2 angles whose sum is 90 o 1 2 35 o A 55 o B <1 & <2 are complementary <A & <B are complementary

9. Supplementary Angles 2 angles whose sum is 180 o 1 2 130 o 50 o X Y <1 & <2 are supplementary. <X & <Y are supplementary.

10. Ex: <A & <B are supplementary. m<A is 5 times m<B. Find m<A & m<B. m<A + m<B = 180 o m<A = 5(m<B) Now substitute! 5(m<B) + m<B = 180 o 6(m<B)=180 o m<B=30 o m<A=150 o