1.6 Angle Pair Relationships

GOAL 1 Identify vertical angles and linear pairs.

GOAL 2 Identify complementary and supplementary angles.

What you should learn

To solve real-life problems, such as finding the measures of angles formed by the cables of a bridge.

Why you should learn it

GOAL 1 VERTICAL ANGLES AND LINEAR PAIRS

1.6 Angle Pair Relationships

Vocabulary

Two angles whose sides form two pairs of opposite rays are called _____________. vertical angles

14 23

Identify the pairs of vertical angles in the diagram.

Click to check.

1 and 3 2 and 4

Two adjacent angles whose noncommon sides are opposite rays are called a _________.linear pair

5 6

common side

noncommon sides

5 and 6 are a linear pair.

EXAMPLE 1

Extra Example 1

EXAMPLE 2

1 5 432

a. Are a linear pair?

b. Are a linear pair?

c. Are vertical angles?

d. Are vertical angles?

Click to see the answers.

1 and 2

5 and 3

4 and 5

1 and 3

yes

no

no

yes

Extra Example 2In one town, Main Street and Columbus Avenue intersect to form an angle of 36°. Find the measures of the other three angles.

Click to see a diagram.

Columbus Avenue

Main Street36°m X

m Y m Z

Click to see the answers.

144

36 144

EXAMPLE 3

Extra Example 3

Solve for x and y. Then find the angle measures.

Click for a hint.

L

M

PN

O

(4 15) x(5 30) x

(3 15) y(3 15) y

180

and 180

m LPM m NPM

m LPO m NPO

Solve each equation to find x and y. Click for the answers.

15, 30 x y m LPM m OPN

m MPN m LPO

75

105

Checkpoint

1. Name one pair of vertical angles and one pair of angles that form a linear pair. Click to see the answers.

J

H

K

GI

(5 30) x(2 4) x

Vertical angle pairs:

Linear pairs:

and ; and IHJ GHK JHK GHI

and ; and ;

and ; and

IHJ JHK JHK KHG

KHG GHI GHI IHJ

2. What is the measure of ?GHI 140

GOAL 2 COMPLEMENTARY AND SUPPLEMENTARY ANGLES

1.6 Angle Pair Relationships

Vocabulary

If the sum of the measures of two angles is 90°, the angles are ______________ angles, and each is the ___________ of the other.

complementarycomplement

21

Note: Complementary angles may or may not be adjacent.

are nownonadjacent complementary angles.

1 and 2

If the sum of the measures of two angles is 180°, the angles are _____________ angles, and each is the ___________ of the other.

EXAMPLE 4

supplementarysupplement

3 4

Note: Supplementary angles may or may not be adjacent.If are adjacent and supplementary, they form a _________.

3 and 4 linear pair

are now nonadjacent supplementary angles, and they no longer form a linear pair.

3 and 4

Extra Example 4

EXAMPLE 5

State whether the two angles are complementary, supplementary, or neither. Click for the solution.

12

39

6

12

39

6

neithersupplementary

neither

Extra Example 5a. Given that is a supplement of

find G , and is 82 , H m G

.m H

Click to see the solution.

U , and is 73 , V m U.m V

b. Given that is a complement of find

Click to see the solution.

180 m G m H82 180 m H

98 m H

90 m U m V

73 90 m V

17 m V

EXAMPLE 6

Extra Example 6

are supplementary. The measure of is half the measure of Find Click for a hint.

and ST T.S .m S

1180 and

2m T m S m T m S

Substitute and solve. Click for the solution.

180m T m S 1

1802m S m S

3180

2m S

120m S

Checkpoint are complements and are supplements. If is four times find the measure of each of the three angles. Click for a hint.

and D E and D F m E ,m D

4( ) and 90m E m D m E m D

Substitute and solve. Click for the answers.

m D

m E

m F

1872162

QUESTIONS?