The Polygon Angle-Sum Theorems

Name

Class

Date

Practice

6-1

Form G

The Polygon Angle-Sum Theorems

Find the sum of the angle measures of each polygon.

1.

2.

3.

540

1080

900

4. 12-gon 1800

5. 18-gon 2880

6. 25-gon 4140

7. 60-gon 10,440

8. 102-gon 18,000

9. 17-gon 2700

10. 36-gon 6120

11. 90-gon 15,840

12. 11-gon 1620

Find the measure of one angle in each regular polygon. Round to the nearest

tenth if necessary.

13.

14.

15.

STOP

128.6

135

108

16. regular 15-gon 156

17. regular 11-gon 147.3

18. regular 13-gon 152.3

19. regular 24-gon 165

20. regular 360-gon 179

21. regular 18-gon 160

22. regular 36-gon 170

23. regular 72-gon 175

24. regular 144-gon 177.5

Algebra Find the missing angle measures.

25.

26.

2x

(2x + 20)

y

(2y  20)

(2x + 20)

2x

80; 100; 80; 100

27.

(2y  20)

28.

x

124

118

100

98

y

100

80; 140; 140; 80; 140; 140

29.

x

(x + 50)

x

(5x  5)

x

(4x  10)

(4x  15) (4x  15)

(x + 50)

100; 100; 150; 100; 150; 150; 150

90; 115; 115; 90; 130

Prentice Hall Gold Geometry ? Teaching Resources

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(4x  10)

Name

Class

Date

Practice (continued)

6-1

Form G

The Polygon Angle-Sum Theorems

Algebra Find the missing angle measures.

A

30.

B 109

G

31.

x 91

E 160

100

D

33.

F

80

C

S

R

x 130

Q 97 130

H

124 150

129

54

133

93

32. L

I

M

130

x

K

J

43

x

34. A

B 47

35.

P 129

48

112

x

E

F

N

127

135 147 G

D

110

128

118 H

T

K

C

U

71

x

J

135

Find the measure of an exterior angle of each regular polygon. Round to the

nearest tenth if necessary.

36. decagon 36

37. 16-gon 22.5

38. hexagon 60

39. 20-gon 18

40. 72-gon 5

41. square 90

42. 15-gon 24

43. 25-gon 14.4

44. 80-gon 4.5

Find the values of the variables for each regular polygon. Round to the nearest

tenth if necessary.

45.

y

x

120; 60

51.4

46.

108; 72

47.

a

n

b

48. Reasoning Can a quadrilateral have no obtuse angles? Explain.

Yes; a rectangle is a quadrilateral with no obtuse angles.

The measure of an exterior angle of a regular polygon is given. Find the measure

of an interior angle. Then find the number of sides.

49. 12 168; 30

50. 6 174; 60

51. 45 135; 8

52. 40 140; 9

53. 24 156; 15

54. 18 162; 20

55. 9 171; 40

56. 14.4 165.6; 25

57. 7.2 172.8; 50

Prentice Hall Gold Geometry ? Teaching Resources

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