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California Standards - PowerPoint PPT Presentation

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

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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

Find each unknown angle measure.

A. The angles are complementary.

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

71° + m1 = 90°

Subtract 71° from both sides.

1

–71°–71°

m1 = 19°

71°

Find each unknown angle measure.

B. The angles are supplementary.

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

125° + m2 = 180°

Subtract 125° from both sides.

–125°–125°

m2 = 55°

125°

2

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.

m3 = 82°

3

82°

B

4

31°

A

E

D

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

D. BEA CED; mAED = 180°

Since BEA and CED are congruent, mCED = 31°.

mBEA + mBEC + mCED = 180°.

The sum of the measures is 180°.

31° + m4 + 31° = 180°

Substitute.

62°+ m4 = 180°

–62°–62°

Subtract 62° from both sides.

m4 = 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° + md = 90°

d

Subtract 65° from both sides.

–65°–65°

md = 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° + ms = 180°

Subtract 145° from both sides.

–145°–145°

ms = 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.

mt = 32°

t

32°

Check It Out! Example 1

Find each unknown angle measure.

D. WZV XZY; mVZY = 180°

X

W

b

Since WZV and XZY are congruent, mXZY = 25°.

mWZV + mWZX + mXZY = 180°

25°

V

Z

Y

The sum of the measures is 180°.

25° + b + 25° = 180°

Substitute.

50°+ b = 180°

Subtract 50° from both sides.

–50°–50°

b = 130°

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°

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°

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.