**Section 1.6**

Angle Pair Relationships

Angle Pair Relationships

Definitions

Vertical Angles

Linear Pairs

Example 2

Example 3

Example 1

Definitions

Vertical Angles- Two angles with sides that form two pairs of opposite rays

Linear Pair- Two adjacent angles with noncommon sides that form opposite rays

Vertical Angles are congruent, so:

<1 is congruent to <3

<2 is congruent to <4

Name: <MNP and <PNO

The m<3 = 55°

2c+4=6c-12

2c+4+12=6c-12+12

2c+16=6c

2c-2c=16=6c-2c

16=4c

16/4=4c/4

c=4

m<2=81° (180°-99°)

**By: Maddie McCleary**

1

2

3

4

and

M

N

O

P

45°

135°

Sum of the angle measures is always 180°

2

55°

1

4

Find the measures of the missing angles

m<1= 125° (180°-55°)

m<2= 55° (Vertical Angles)

m<4= 125° (180°-55°)

Solve for C and find the missing angles.

(2c+4)°

(6c-12)°

2(4)+4=12°

6(4)-12=12°

99°

2

The measure of angle 1 is 99°, find the measure of angle 2.

Complementary: Two angles with a sum of 90°

Supplementary: Two angles with a sum of 180°

Example 4

<C and <M are Complementary. If m<M=65°, find m<C.

M

C

m<C=25° (90°-65°)

Example 5

Find the values of the variables

135°

(2r+35)°

1

2

3

4

s °

s°

2r+35=135

2r+35-35=135-35

2r=100

2r/2=100/2

r=50°

**The angles are considered to be adjacent if they are directly touching each other. Supplementary and Complementary angles can either be adjacent or nonadjacent.

s+50=180

s+50-50=180-50

s=130°