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# 8-3 - PowerPoint PPT Presentation

8-3. Angle Relationships. Course 1. Warm Up. Problem of the Day. Lesson Presentation. Warm Up Identify the type of angle. 1. 70° 2. 90° 3. 140° 4. 180°. acute. right. obtuse. straight. Problem of the Day

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8-3

Angle Relationships

Course 1

Warm Up

Problem of the Day

Lesson Presentation

Warm Up

Identify the type of angle.

1.70°

2. 90°

3. 140°

4. 180°

acute

right

obtuse

straight

Problem of the Day

A line forms an angle of 57° with the vertical axis. What angle does the line form with the horizontal axis?

33° or 147°

Vocabulary

congruent

vertical angles

complementary angles

supplementary angles

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

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

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

Additional Example 1A: Identifying Types of Angle Pairs

Identify the type of each angle pair shown.

5 6

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

They are vertical angles.

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.

7 8

Check It Out: Example 1A

Identify the type of each angle pair shown.

3 and 4 are side by side and have a common vertex and ray.

3

4

Check It Out: Example 1B

Identify the type of each angle pair shown.

7

8

7 and 8 are opposite each other and are formed by two intersecting lines.

They are vertical angles.

L

N

65°

25°

M

P

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

65° + 25° = 90°

LMN and NMP are complementary.

K

65°

115°

G

J

H

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

65° + 115° = 180°

GHK and KHJ are supplementary.

Additional Example 2A: Identifying an Unknown Angle Measure

Find each unknown angle measure.

The angles are complementary.

The sum of the measures is 90°.

71° + 1 = 90°

1

–71°–71°

m1 = 19°

71°

Additional Example 2B: Identifying an Unknown Angle Measure

Find each unknown angle measure.

The angles are supplementary.

The sum of the measures is 180°.

125° + 2 = 180°

–125°–125°

m2 = 55°

125°

2

Additional Example 2C: Identifying an Unknown Angle Measure

Find each unknown angle measure.

The angles are vertical angles.

3

82°

m3 = 82°

Vertical angles are congruent.

M

L

80°

x

y

J

K

N

Additional Example 2D: Identifying an Unknown Angle Measure

Find each unknown angle measure.

JKL and MKN are congruent.

x + y + 80° = 180°

The sum of the measures is 180°.

–80°–80°

x + y = 100°

Each angle measures half of 100°.

x = 50° and y = 50°

Check It Out: Example 2A

Find each unknown angle measure.

The angles are complementary.

65° + d = 90°

The sum of the measures is 90°.

d

–65°–65°

md = 25°

65°

Check It Out: Example 2B

Find each unknown angle measure.

The angles are supplementary.

145° + s = 180°

The sum of the measures is 180°.

–145°–145°

ms = 35°

145°

s

Check It Out: Example 2C

Find each unknown angle measure.

The angles are vertical angles.

t

Vertical angles are congruent.

mt = 32°

32°

C

D

50°

x

y

A

B

E

Check It Out: Example 2D

Find each unknown angle measure.

ABC andDBE are congruent.

x + y + 50° = 180°

The sum of the measures is 180°.

–50°–50°

x + y = 130°

Each angle measures half of 130°.

x = 65° and y = 65°

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.

6

7