1-3

Pairs of Angles

Adjacent Angles

A pair of angles with a shared vertex and common side but do not have overlapping interiors. 1 and 2 are adjacent. 3 and 4 are not. 1 and ADC are not adjacent.

Adjacent Angles( a common side ) Non-Adjacent Angles

22°36°

21D

B

C

A 43

Definition:

Examples:

Complementary AnglesA pair of angles whose sum is 90˚Definition:

Examples:

Adjacent Angles( a common side )

21

Q

AB

C 1

2

QR

AB

F

G

Non-Adjacent Angles

m1 = 40°m2 = 50°

Supplementary AnglesA pair of angles whose sum is 180˚Definition:

Examples:

Adjacent supplementary angles are also called “Linear Pair.”

Non-Adjacent Angles

2 1

A Q

B

C

1

2

A QR

BF

Gm2 = 140°m1 = 40°

Vertical AnglesA pair of angles whose sides form opposite rays.Definition:

4

3

2

1A

Q

D

B

C

Examples:

2 and 4

1 and 3

Vertical angles are non-adjacent angles formed by intersecting lines.

Example: If m4 = 67º, find the measures of all other angles.

4 3

2 1

Example: If m1 = 23 º and m2 = 32 º, find the measures of all other angles.

6 5

4 3 2

1

Example: If m1 = 44º, m7 = 65º find the measures of all other angles.

7

6 5 4

3

2 1