Holt CA Course 1

8-3 Angle Relationships

Warm Up

California StandardsCalifornia Standards

Lesson Presentation

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Holt CA Course 1

8-3 Angle RelationshipsWarm UpComplete each sentence.

1. Angles whose measures have a sum of 90° are _______________ .

2. A part of a line that starts at one point and extends forever in one direction is called a _______.

3. Angles whose measures have a sum of 180° are ______________.

4. A part of a line between two points is called a ____________.

complementary

ray

supplementary

segment

Holt CA Course 1

8-3 Angle Relationships

Review of Grade 6 MG2.2 Use properties of

complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.Also covered: 6MG2.1

California Standards

Holt CA Course 1

8-3 Angle RelationshipsAdditional Example 1: Finding Angle Measures

Use the diagram to find each angle measure.

A. If m1 = 37°, find m3.

1 and 2 are supplementary.

The measures of 2 and 3 are supplementary.

m2 = 180° – 37° = 143°

m3 = 180° – 143° = 37°

So m1 = m3, or 1 3.

Holt CA Course 1

8-3 Angle Relationships

The symbol for congruence is =, which is read as “is congruent to.”

Writing Math ~

Holt CA Course 1

8-3 Angle Relationships

B. If m4 = y°, find m2.

m3 = 180° – y°

m2 = 180° – m3

= 180° – 180° + y°

= y°

Substitute 180o – yo for m3.

So m4 = m2, or 4 2.

Additional Example 1: Finding Angle Measures

Use the diagram to find each angle measure.

3 and 4 are supplementary.

2 and 3 are supplementary.

= 180° – (180o – yo)

Distributive Property

Simplify.

Holt CA Course 1

8-3 Angle Relationships

A. If m1 = 42°, find m3.1

23

4

Check It Out! Example 1

The measures of 1 and 2 are supplementary.

The measures of 2 and 3 are supplementary.

m2 = 180° – 42° = 138°

m3 = 180° – 138° = 42°

So m1 = m3, or 1 3.

Use the diagram to find each angle measure.

Holt CA Course 1

8-3 Angle Relationships

m3 = 180° – x°

m2 = 180° – m3

= 180° – 180° + x°

= x°

Substitute 180o – xo for m3.

So m4 = m2, or 4 2.

Check It Out! Example 1Use the diagram to find each angle measure.

3 and 4 are supplementary.

2 and 3 are supplementary.

= 180° – (180o – xo)

Distributive Property

Simplify.

B. If m4 = x°, find m2.

1

23

4

Holt CA Course 1

8-3 Angle Relationships

The angles in Example 1 are examples of adjacent angles and vertical angles. These angles have special relationships because of their positions.

Adjacent angles have a common vertex and a common side, but no common interior points.

Vertical angles are the nonadjacent angles formed by two intersecting lines.

Holt CA Course 1

8-3 Angle Relationships

A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angle pairs with special properties.

Holt CA Course 1

8-3 Angle Relationships

Holt CA Course 1

8-3 Angle Relationships

In the figure, line l || line m. Find the measure of the angle.

Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals

A.4

m4 = 124°

Corresponding angles are congruent.

Holt CA Course 1

8-3 Angle Relationships

B.2

m2 + 124° = 180°

2 is supplementary to the 124° angle.

m2 = 56°

–124° –124° Subtract.

Simplify.

In the figure, line l || line m. Find the measure of the angle.

Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals

Holt CA Course 1

8-3 Angle Relationships

2 and 6 are corresponding angles.C6

m6 = 56°

In the figure, line l || line m. Find the measure of the angle.

Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals

Holt CA Course 1

8-3 Angle Relationships

Check It Out! Example 2

A.7

m7 = 144°

1 144°3 4

5 67 8

m

n

In the figure, line l || line m. Find the measure of the angle.

Alternate exterior angles are congruent.

Holt CA Course 1

8-3 Angle Relationships

B.1

m1 + 144° = 180°

1 is supplementary to the 144° angle.

m1 = 36°–144° –144° 1 144°

3 45 6

7 8

m

n

Check It Out! Example 2

In the figure, line l || line m. Find the measure of the angle.

Holt CA Course 1

8-3 Angle Relationships

C.6

m6 = 144°1 144°

3 45 6

7 8

m

n

Check It Out! Example 2

In the figure, line l || line m. Find the measure of the angle.

Corresponding angles are congruent.

Holt CA Course 1

8-3 Angle RelationshipsLesson Quiz

In the figure, line a || line b.

1. Name all angles congruent to 3.

2. Name all the angles supplementary to 6.

3. If m1 = 105° what is m3?

4. If m5 = 120° what is m2?

1, 5, 7

1, 3, 5, 7

105°

60°