1. 1.6 Angle Pair Relationships

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

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

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 2

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

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

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

8. Complementary Angles 2 angles whose sum is 90o1 2
55o A
<1 & <2 are complementary
<A & <B are complementary B

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

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