Holt CA Course 1

9-7 Angle Measures in Triangles

MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.Also covered: AF1.1, MG2.1

California Standards

Holt CA Course 1

9-7 Angle Measures in Triangles

If you tear off the corners of a triangle and put all three of them together, you will find that they form a straight angle. This suggests that the sum of the measures of the angles in a triangle is 180°.

Holt CA Course 1

9-7 Angle Measures in Triangles

Angles of a Triangle

The sum of the measures of the angles in a triangle is 180°.

m1 + m2 + m3 = 180°

1 3

2

Holt CA Course 1

9-7 Angle Measures in Triangles

A. Find the unknown angle measure in each triangle.

Additional Example 1: Finding an Angle Measure of in a Triangle

55°

80° x

80° + 55° + x = 180°

135° + x = 180°

–135° –135°

x = 45°

The measure of the unknown angle is 45°.

The sum of the angle measures in a triangle is 180°.

Add 55° and 80°.

Subtract 135° from both sides.

Holt CA Course 1

9-7 Angle Measures in Triangles

B. Find the unknown angle measure in each triangle.

Additional Example 1: Finding an Angle Measure of in a Triangle

34°

x

34° + 90° + x = 180°

124° + x = 180°

–124° –124°

x = 56°

The measure of the unknown angle is 56°.

The sum of the angle measures in a triangle is 180°.

Add 34° and 90°.

Subtract 124° from both sides.

Holt CA Course 1

9-7 Angle Measures in Triangles

A. Find the unknown angle measure in the triangle.

Check It Out! Example 1

90° + 30° + x = 180°

120° + x = 180°

–120° –120°

x = 60°

The measure of the unknown angle is 60°.

The sum of the angle measures in a triangle is 180°.

Add 30° and 90°.

Subtract 120° from both sides.

30°

x

Holt CA Course 1

9-7 Angle Measures in Triangles

B. Find the unknown angle measure in each triangle.

Check It Out! Example 1

22°

x

22° + 90° + x = 180°

112° + x = 180°

–112° –112°

x = 68°

The measure of the unknown angle is 68°.

The sum of the angle measures in a triangle is 180°.

Add 22° and 90°.

Subtract 112° from both sides.

Holt CA Course 1

9-7 Angle Measures in Triangles

The figure shows part of the support structure of a bridge. Find the unknown angle measure x. Show your work.

75°

110°x

Substitute 110° for mDEC.

Subtract 110° from both sides.

Step 1: Find the measure of DEA.

mDEA + mDEC = 180°

mDEA + 110° = 180°

mDEA = 70°

A B

CD

E

Additional Example 2: Application

Holt CA Course 1

9-7 Angle Measures in Triangles

The figure shows part of the support structure of a bridge. Find the unknown angle measure x. Show your work.

Additional Example 2 Continued

x

Sum of angle measures is 180°.

Add 70° and 75°.

Step 2: Find the angle measure x.

70° + 75° + x = 180°

145° + x = 180°

x = 35°

A B

CD

E

Subtract 145° from both sides.

75°

110°

Holt CA Course 1

9-7 Angle Measures in Triangles

The figure shows a diagram of a design. Find the unknown angle measure x. Show your work. 65°

95°

x

Substitute 95° for mDEA.

Subtract 95° from both sides.

Step 1: Find the measure of DEC.

mDEC + mDEA = 180°

mDEC + 95° = 180°

mDEC = 85°

A B

CD

E

Check It Out! Example 2

Holt CA Course 1

9-7 Angle Measures in Triangles

Check It Out! Example 2 Continued

Sum of angle measures is 180°.

Add 85° and 65°.

Step 2: Find the angle measure x.

85° + 65° + x = 180°

150° + x = 180°

x = 30°

Subtract 150° from both sides.

65°

95°

x

A B

CD

E

The figure shows a diagram of a design. Find the unknown angle measure x. Show your work.