warm up identify the type of angle. 1. 70° 2. 90° 3. 140° 4. 180°

8-3 Angle Relationships

Warm UpIdentify the type of angle.

1. 70°

2. 90°

3. 140°

4. 180°

acute

right

obtuse

straight

8-3 Angle Relationships

Learn to understand relationships of angles.

8-3 Angle Relationships

Vocabulary

congruentvertical anglesadjacent anglescomplementary anglessupplementary angles

8-3 Angle Relationships

Congruent angles have the same measure.

Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent.

MRP and NRQ are vertical angles.

MRN and PRQ are vertical angles

8-3 Angle Relationships

Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent.

MRN and NRQ are adjacent angles. They share vertex R and RN.

NRQ and QRP are adjacent angles. They share vertex R and RQ.

8-3 Angle Relationships

Additional Example 1A: Identifying Types of Angle Pairs

Identify the type of each angle pair shown.

5 and 6 are opposite each other and are formed by two intersecting lines.

They are vertical angles.

5 6

8-3 Angle Relationships

Additional Example 1B: Identifying Types of Angle Pairs

Identify the type of each angle pair shown.

7 and 8 are side by side and have a common vertex and ray.

They are adjacent angles.

7 8

8-3 Angle Relationships

65° + 25° = 90°

LMN and NMP are complementary.

Complementary angles are two angles whose measures have a sum of 90°.

8-3 Angle Relationships

Supplementary angles are two angles whose measures have a sum of 180°.

65° + 115° = 180°

GHK and KHJ are supplementary.

8-3 Angle Relationships

Additional Example 2A: Identifying an Unknown Angle Measure

Find each unknown angle measure.

71° + 1 = 90°–71° –71°

m1 = 19°

The sum of the measures is 90°.

1

71°

The angles are complementary.

8-3 Angle Relationships

Additional Example 2B: Identifying an Unknown Angle Measure

Find each unknown angle measure.

125° + 2 = 180°–125° –125°

m2 = 55°

The sum of the measures is 180°.

2125°

The angles are supplementary.

8-3 Angle Relationships

Additional Example 2C: Identifying an Unknown Angle Measure

Find each unknown angle measure.

m3 = 82° Vertical angles are congruent.

3 82°

The angles are vertical angles.

8-3 Angle Relationships

Additional Example 2D: Identifying an Unknown Angle Measure

Find each unknown angle measure.

x + y + 80° = 180°–80° –80°

x + y = 100°

The sum of the measures is 180°.

JKL and MKN are congruent.

x = 50° and y = 50° Each angle measures half of 100°.

x 80°

K

ML

NJ

y

8-3 Angle Relationships

Lesson Quiz

1. Identify the type of angle pair shown.

Find each unknown angle measure.

2. The angles are vertical angles.

3. The angles are supplementary.

adjacent

d = 130°

67

x = 45°

d

130°

x 135°

8-3 Angle Relationships

1. Identify the type of angle pair shown.

A. complementary

B. supplementary

C. adjacent

D. vertical

Lesson Quiz for Student Response Systems

AB

8-3 Angle Relationships

2. Identify the unknown angle measure if the angles are complementary.

A. 40

B. 50

C. 90

D. 140

Lesson Quiz for Student Response Systems

40A

8-3 Angle Relationships

3. Identify the unknown angle measure if the angles are supplementary.

A. y = 145

B. y = 125

C. y = 90

D. y = 35

Lesson Quiz for Student Response Systems

55A