1. 9-6 Finding Angle Measures in Polygons Warm Up Problem of the Day
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Warm Up
Problem of the Day
Lesson Presentation

2. 9-6 Finding Angle Measures in Polygons Warm Up Solve. 1. n + 9 = 37
Course 1
9-6
Finding Angle Measures in Polygons
Warm Up
Solve.
1. n + 9 = 37
2. 6 = n - 20
3. 11n = 121
4. 7 =
n = 28
n = 26
n = 11
n 7
n = 49

3. 9-6 Finding Angle Measures in Polygons Problem of the Day
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9-6
Finding Angle Measures in Polygons
Problem of the Day
If a triangle has two angles that measure 41° and 117°, what is the measure of the third angle?
22°

4. 9-6 Learn to find angle measures in polygons.
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9-6
Finding Angle Measures in Polygons
Learn to find angle measures in polygons.

5. Additional Example 1: Subtracting to Find Angle Measures
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9-6
Finding Angle Measures in Polygons
Additional Example 1: Subtracting to Find Angle Measures
Use a protractor to find the measure of XYZ. Then classify the angle. X Z Y
Place the center point of the protractor on the vertex of the angle.

6. Additional Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle. X Z Y
Read the measures where ray XY and ray YZ cross.

7. 9-6 Finding Angle Measures in Polygons Caution!
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9-6
Finding Angle Measures in Polygons
Ray XY can also be read as crossing at 30°, and ray YZ can be read at crossing at 110°, The angle measure is still the same. Make sure that you read the measures on the same scale.
Caution!

8. Additional Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle. X Z Y
Ray XY crosses at 150°, and ray YZ crosses at 70°.

9. Additional Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle. X Z Y
The measure of XYZ is 150° - 70°, or 80°. Write this as mXYZ = 80°.

10. Additional Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle. X Z Y
Since 80°< 90°, the angle is acute.

11. Additional Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle. X Z
Check
Use the other scale on the protractor to find the measure of XYZ. 110° - 30° = 80°. Y

12. 9-6 Finding Angle Measures in Polygons Check It Out: Example 1
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9-6
Finding Angle Measures in Polygons
Check It Out: Example 1
Use a protractor to find the measure of LMN. Then classify the angle. N L M
Place the center point of the protractor on the vertex of the angle.

13. Check It Out: Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle. N L M
Read the measures where ray LM and ray MN cross.

14. Check It Out: Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle. N L M
Ray LM crosses at 50°, and ray MN crosses at 160°.

15. Check It Out: Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle. N L M
The measure of LMN is 160° - 50°, or 110°. Write this as m LMN = 110°.

16. Check It Out: Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle. N L M
Since 110° > 90°, the angle is obtuse.

17. Check It Out: Example 1 Continued
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9-6
Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle. N L
Check
Use the other scale on the protractor to find the measure of LMN. 130° - 20° = 110°. M

18. 9-6 Finding Angle Measures in Polygons
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9-6
Finding Angle Measures in Polygons
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.

19. Additional Example 2: Estimating Angle Measures
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9-6
Finding Angle Measures in Polygons
Additional Example 2: Estimating Angle Measures
Estimate the measure of K in parallelogram JKLM. Then use a protractor to check the reasonableness of your answer. L M J K
Think: The measure of the angle is close to 150°.

20. Additional Example 2 Continued
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Finding Angle Measures in Polygons
Additional Example 2 Continued L M J K
Use the protractor. The measure of the angle is 145°. mK = 145°, so the estimate is reasonable.
Use the scale on the protractor that starts with 0°.
Caution!

21. 9-6 Finding Angle Measures in Polygons Check It Out: Example 2
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Finding Angle Measures in Polygons
Check It Out: Example 2
Estimate the measure of D in parallelogram ABCD. Then use a protractor to check the reasonableness of your answer. D A B C
Think: The measure of the angle is close to 50°.

22. Check It Out: Example 2 Continued
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Finding Angle Measures in Polygons
Check It Out: Example 2 Continued D A B C
Use the protractor. The measure of the angle is 53°. mD = 53°, so the estimate is reasonable.

23. Additional Example 3: Sports Application
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Finding Angle Measures in Polygons
Additional Example 3: Sports Application
The shape of a softball home plate is shown below. Find the measures of C and E. A B E C D
Use a protractor to measure C.
CB crosses at 130°, and CD crosses at 40°.
Subtract. 130° – 40° = 90°
C = 90°

24. Additional Example 3 Continued
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Finding Angle Measures in Polygons
Additional Example 3 Continued
The shape of a softball home plate is shown below. Find the measures of C and E.
Estimate the mE.
It is greater than 90°, so it looks as if the angle measure is 90° + 45°.
So, mE is about 135°. A B E C D
Use a protractor to measure E.
E = 135°

25. 9-6 Finding Angle Measures in Polygons Check It Out: Example 3
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Finding Angle Measures in Polygons
Check It Out: Example 3
A 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° A B C D
A = 70°

26. Check It Out: Example 3 Continued
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9-6
Finding Angle Measures in Polygons
Check It Out: Example 3 Continued
A quadrilateral is shown below. Find the measures of A and C.
Estimate the mC.
It is greater than 90°, so it looks as if the angle measure is 90° + 20°.
So, mC is about 110°. A B C D
Use a protractor to measure C.
C = 110°

27. Insert Lesson Title Here
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Finding Angle Measures in Polygons
Insert Lesson Title Here
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

28. Insert Lesson Title Here
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Finding Angle Measures in Polygons
Insert Lesson Title Here
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.
45°