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California Standards

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California

Standards

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

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

A. The angles are complementary.

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

71° + m1 = 90°

Subtract 71° from both sides.

1

–71°–71°

m1 = 19°

71°

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

B. The angles are supplementary.

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

125° + m2 = 180°

Subtract 125° from both sides.

–125°–125°

m2 = 55°

125°

2

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

C. The angles are vertical angles.

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

Congruent angles have the same measure.

m3 = 82°

3

82°

C

B

4

31°

A

E

D

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

D. BEA CED; mAED = 180°

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

mBEA + mBEC + mCED = 180°.

The sum of the measures is 180°.

31° + m4 + 31° = 180°

Substitute.

62°+ m4 = 180°

Add.

–62°–62°

Subtract 62° from both sides.

m4 = 118°

Check It Out! Example 1

Find each unknown angle measure.

A. The angles are complementary.

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

65° + md = 90°

d

Subtract 65° from both sides.

–65°–65°

md = 25°

65°

Check It Out! Example 1

Find each unknown angle measure.

B. The angles are supplementary.

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

145° + ms = 180°

Subtract 145° from both sides.

–145°–145°

ms = 35°

145°

s

Check It Out! Example 1

Find each unknown angle measure.

C. The angles are vertical angles.

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

Congruent angles have the same measure.

mt = 32°

t

32°

Check It Out! Example 1

Find each unknown angle measure.

D. WZV XZY; mVZY = 180°

X

W

b

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

mWZV + mWZX + mXZY = 180°

25°

V

Z

Y

The sum of the measures is 180°.

25° + b + 25° = 180°

Substitute.

50°+ b = 180°

Add.

Subtract 50° from both sides.

–50°–50°

b = 130°

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.

The sum of the measures is 90°.

27°+ c = 90°

–27°–27°

Subtract 27° from both sides.

c = 63°

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.

The sum of the measures is 180°.

151°+ a = 180°

–151°–151°

Subtract 151° from both sides.

a = 29°

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.

b = 27°

Vertical angles are congruent.

165°

y

x

22°

z

Check It Out! Example 2

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

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

The sum of the measures is 90°.

22°+ z = 90°

–22°–22°

Subtract 22° from both sides.

z = 68°

165°

y

x

22°

z

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.

The sum of the measures is 180°.

165°+ x = 180°

–165°–165°

Subtract 165° from both sides.

x = 15°

165°

y

x

22°

z

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.

y = 22°

Vertical angles are congruent.