8-3

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8-3 Angle Relationships8-3 Angle Relationships

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

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8-3 Angle Relationships

Warm UpIdentify the type of angle.

1. 70°

2. 90°

3. 140°

4. 180°

acute

right

obtuse

straight

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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°

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Learn to understand relationships of angles.

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Vocabulary

congruentvertical anglesadjacent anglescomplementary anglessupplementary angles

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When angles have the same measure, they are said to be congruent.

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

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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.

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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

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Additional Example 1B: Identifying Types of Angle Pairs


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

They are adjacent angles.

7 8

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Check It Out: Example 1A


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

They are adjacent angles.

3

4

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Check It Out: Example 1B


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

They are vertical angles.

7

8

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65° + 25° = 90°

LMN and NMP are complementary.

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

P

N

M

L

25°65°

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

65° + 115° = 180°

GHK and KHJ are supplementary.

J

K

H

115°65°

G

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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.

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Additional Example 2B: Identifying an Unknown Angle Measure


125° + 2 = 180°–125° –125°

m2 = 55°


2125°

The angles are supplementary.

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Additional Example 2C: Identifying an Unknown Angle Measure


m3 = 82° Vertical angles are congruent.

3 82°

The angles are vertical angles.

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Additional Example 2D: Identifying an Unknown Angle Measure


x + y + 80° = 180°–80° –80°

x + y = 100°


JKL and MKN are congruent.

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

x 80°

K

ML

NJ

y

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Check It Out: Example 2A


65° + d = 90°–65° –65°

md = 25°


d

65°

The angles are complementary.

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Check It Out: Example 2B


145° + s = 180°–145° –145°

ms = 35°


s145°

The angles are supplementary.

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Check It Out: Example 2C


mt = 32° Vertical angles are congruent.

t

32°

The angles are vertical angles.

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Check It Out: Example 2D


x + y + 50° = 180°–50° –50°

x + y = 130°


ABC and DBE are congruent.

x = 65° and y = 65° Each angle measures half of 130°.

x50°

B

DC

EA

y

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Lesson Quiz

1. Identify the type of angle pair shown.


2. The angles are vertical angles.

3. The angles are supplementary.

adjacent

d = 130°

67

x = 45°

d

130°

x 135°

8-3

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