Holt CA Course 1

9-4 Finding Angle Measures

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Holt CA Course 1

9-4 Finding Angle Measures

Warm UpTell whether the given angles are vertical, complementary, or supplementary.

1. QXT and QXR

2. QXR and TXS

3. PXQ and QXR

4. PXQ and PXS

5. TXS and SXR

supplementary

vertical

complementary

supplementary

supplementary

Holt CA Course 1

9-4 Finding Angle Measures

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

9-4 Finding Angle Measures

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

71° + m1 = 90°–71° –71°

m1 = 19°

Since the angles are complementary, the sum of the angle measures is 90°.

1

71°

A. The angles are complementary.

Subtract 71° from both sides.

Holt CA Course 1

9-4 Finding Angle Measures

125° + m2 = 180°–125° –125°

m2 = 55°

Subtract 125° from both sides.

2125°

B. The angles are supplementary.

Since the angles are supplementary, the sum of the angle measures is 180°.

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

Holt CA Course 1

9-4 Finding Angle Measures

m3 = 82° Congruent angles have the same measure.

3 82°

C. The angles are vertical angles.

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

Since the angles are vertical angles, the angles are congruent.

Holt CA Course 1

9-4 Finding Angle Measures

–27° –27°27° + c = 90° The sum of the measures is 90°.

c = 63°

Subtract 27° from both sides.

Additional Example 2: Application

Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work.

Step 1: The angles labeled c and 27° are complementary. To find c, use properties of complementary angles.

Holt CA Course 1

9-4 Finding Angle Measures

–151° –151°

151° + a = 180° The sum of the measures is 180°.

a = 29°

Subtract 151° from both sides.

Additional Example 2 Continued

Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work.

Step 2: The angles labeled a and 151° are supplementary. To find a, use properties of supplementary angles.

Holt CA Course 1

9-4 Finding Angle Measures

b = 27° Vertical angles are congruent.

Additional Example 2 Continued

Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work.

Step 3: The angles labeled b and 27° are vertical angles. To find b, use properties of vertical angles.

Holt CA Course 1

9-4 Finding Angle Measures

Check It Out! Example 1

Find each unknown angle measure.

65° + md = 90°–65° –65°

md = 25°

Subtract 65° from both sides.

d

65°

A. The angles are complementary.

Since the angles are complementary, the sum of the angle measures is 90°.

Holt CA Course 1

9-4 Finding Angle Measures

–22° –22°22° + z = 90° The sum of the measures is 90°.

z = 68°Subtract 22° from both sides.

Check It Out! Example 2

Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work.

x 165°22°

z

y

Step 1: The angles labeled z and 22° are complementary. To find z, use properties of complementary angles.

Holt CA Course 1

9-4 Finding Angle Measures

–165° –165°

165° + x = 180° The sum of the measures is 180°.

x = 15°

Subtract 165° from both sides.

Check It Out! Example 2 Continued

Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work.

Step 2: The angles labeled x and 165° are supplementary. To find x, use properties of supplementary angles.

x 165°22°

z

y

Holt CA Course 1

9-4 Finding Angle Measures

y = 22° Vertical angles are congruent.

Check It Out! Example 2 Continued

Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work.

Step 3: The angles labeled y and 22° are vertical angles. To find y, use properties of vertical angles.

x 165°22°

z

y

Holt CA Course 1

9-4 Finding Angle Measures

Lesson Quiz: Part I

Find each unknown angle measure.

1. The angles are vertical angles.

2. The angles are supplementary.

d = 130°

x = 45°

Holt CA Course 1

9-4 Finding Angle MeasuresLesson Quiz: Part II

p = 78°

3. KNL = LNM; mJNM = 180°

4. Use the information in the diagram to find

the unknown angle measures a, b, and c.

Show your work.

<

a = 147°, b = 123°, c = 19°

Holt CA Course 1

9-4 Finding Angle Measures

31° + m4 + 31° = 180°

–62° –62° 62° + m4 = 180°

The sum of the measures is 180°.

D. BEA CED; mAED = 180°

m4 = 118°

Subtract 62° from both sides.

431°E

CB

DA

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

Since BEA and CED are congruent, mCED = 31°.

mBEA + mBEC + mCED = 180°.

Add.

Substitute.

Holt CA Course 1

9-4 Finding Angle Measures

Check It Out! Example 1

Find each unknown angle measure.

145° + ms = 180°–145° –145°

ms = 35°

Subtract 145° from both sides.

s145°

B. The angles are supplementary.

Since the angles are supplementary, the sum of the angle measures is 180°.

Holt CA Course 1

9-4 Finding Angle Measures

Check It Out! Example 1

Find each unknown angle measure.

mt = 32° Congruent angles have the same measure.

t

32°

C. The angles are vertical angles.

Since the angles are vertical angles, the angles are congruent.

Holt CA Course 1

9-4 Finding Angle Measures

25° + b + 25° = 180°

–50° –50°

50° + b = 180°

The sum of the measures is 180°.

D. WZV XZY; mVZY = 180°

b = 130°

Subtract 50° from both sides.

Check It Out! Example 1

Find each unknown angle measure.

Since WZV and XZY are congruent, mXZY = 25°.

mWZV + mWZX + mXZY = 180°

Add.

Substitute.

b25°Z

XW

YV