9-6 Finding Angle Measures in Polygons Course 1 Warm Up Warm Up Lesson Presentation Lesson...

9-6 Finding Angle Measures in Polygons

Course 1

Warm UpWarm Up

Lesson PresentationLesson PresentationProblem of the DayProblem of the Day

Warm UpSolve.1. n + 9 = 37

2. 6 = n - 20

3. 11n = 121

4. 7 =

n = 28

n = 26

Course 1

9-6 Finding Angle Measures in Polygons

n = 11

n = 49n 7

Problem of the DayIf a triangle has two angles that measure 41° and 117°, what is the measure of the third angle?22°

Course 1

9-6 Finding Angle Measures in Polygons

Learn to find angle measures in polygons.

Course 1

9-6 Finding Angle Measures in Polygons

Course 1

9-6 Finding Angle Measures in Polygons

• Ray XY crosses at 150°, and ray YZ crosses at 70°.

Y

X

Z

Additional Example 1 Use a protractor to find the measure of XYZ . Then classify the angle.

Course 1

9-6 Finding Angle Measures in Polygons

Y

X

Z

• The measure of XYZ is 150° 70°, or 80°. Write this as mXYZ = 80°.

Additional Example 1 ContinuedUse a protractor to find the measure of XYZ . Then classify the angle.

Course 1

9-6 Finding Angle Measures in Polygons

Y

X

Z

• Since 80°< 90°, the angle is acute.

Additional Example 1 ContinuedUse a protractor to find the measure of XYZ . Then classify the angle.

Course 1

9-6 Finding Angle Measures in Polygons

Y

X

Z

CheckUse the other scale on the protractor to find the measure ofXYZ. 110° - 30° = 80°.

Additional Example 1 ContinuedUse a protractor to find the measure of XYZ . Then classify the angle.

To estimate the measure of an angle, compare it with an angle whose measure you already know. A right angle has half the measure of a straight angle. A 45° angle has half the measure of a right angle.

Course 1

9-6 Finding Angle Measures in Polygons

Additional Example 2: Estimating Angle MeasuresEstimate the measure of K in parallelogram JKLM. Then use a protractor to check the reasonableness of your answer.

Think: The measure of the angle is close to 150°.

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9-6 Finding Angle Measures in Polygons

L

M J

K

Additional Example 2 Continued

Use the protractor. The measure of the angle is 145°. mK = 145°, so the estimate is reasonable.

Use the scale on the protractor that starts with 0°.

Caution!

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9-6 Finding Angle Measures in Polygons

L

M J

K

Check It Out: Example 2Estimate the measure of D in parallelogram ABCD. Then use a protractor to check the reasonableness of your answer.

Think: The measure of the angle is close to 50°.

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9-6 Finding Angle Measures in Polygons

D

A B

C

Check It Out: Example 2 Continued

Use the protractor. The measure of the angle is 53°. mD = 53°, so the estimate is reasonable.

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9-6 Finding Angle Measures in Polygons

D

A B

C

Additional Example 3: Sports ApplicationThe shape of a softball home plate is shown below. Find the measures of C and E.

Use a protractor to measure C. CB crosses at 130°, and CD crosses at 40°.Subtract. 130° – 40° = 90°

Course 1

9-6 Finding Angle Measures in Polygons

A

BE

CD

C = 90°

Additional Example 3 ContinuedThe shape of a softball home plate is shown below. Find the measures of C and E.

Estimate the mE. It is greater than 90°, so it looks as if the angle measure is 90° + 45°.So, mE is about 135°.

Course 1

9-6 Finding Angle Measures in Polygons

A

BE

CDUse a protractor to measure E.

E = 135°

Check It Out: Example 3A quadrilateral is shown below. Find the measures of A and C.

Use a protractor to measure A. AB crosses at 40°, and AD crosses at 110°.Subtract. 110° 40° = 70°

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9-6 Finding Angle Measures in Polygons

A = 70°

A B

CD

Check It Out: Example 3 ContinuedA quadrilateral is shown below. Find the measures of A and C.

Estimate the mC. It is greater than 90°, so it looks as if the angle measure is 90° + 20°.So, mC is about 110°.

Course 1

9-6 Finding Angle Measures in Polygons

Use a protractor to measure C.

C = 110°

A B

CD

Lesson Quiz: Part I

Solve each equation.

1. Use the protractor to the measure of ABC. Tell what type of angle it is.

120°, obtuse

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9-6 Finding Angle Measures in Polygons

Lesson Quiz: Part II

Solve each equation.

2. Estimate the measure of B in the parallelogram for Exercise 12 on page 512 of your textbook. Then use a protractor to check the reasonableness of your answer.

Insert Lesson Title Here

45°

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9-6 Finding Angle Measures in Polygons