# 3.4B Regular Polygon Angles ANSWERS

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```					Geometry                          3.4B Regular Polygon Angles                          Name ___________________________
Completed:____ Correct:____ Grade:_____/10                                             Period _______ Date ______________

Find the measures of the angles of the
Using the information in the drawings, find the                              triangles.
value of x.
(5x  2)
1.                              2.         2x  (x  3)                     7.                                   8.         (x  11)
20
x                 (x  10) (x  2)
2x 
(6x  4)                  (x  29)
x
2x                                                                                         (4x  20)
(7x  6)
x
x = 10                               x = 20
x = 100                                              x = 69
angles: 64°, 64°, 52°           angles: 31°, 49°, 100°

x                         9. Find the measure of an interior and an
3. (3x  10)                             4.
2x        exterior angle of a regular hexagon.
x
75
45                                                      Each Interior = 120
(x  10)
70                                                                     Each Exterior = 60
(5x  20)
(x  10)            (3x  17)
10. Find the measure of an interior and an
exterior angle of a regular decagon.

x = 47.5                                  x = 79.7                                 Each Interior = 144
Each Exterior = 36

x          11. Find the measure of an interior and an
5. 2x               x                   6.
exterior angle of a regular nonagon.
(2x  5)

Each Interior = 140
2x 
(x  30)                           Each Exterior = 40
30
40
Using the given information in the following
drawings to find the value of x and y.
12.             13.                      14.
70                      x                       55
x = 93                                               x = 75

x           y         120         y          x          y

x = 125                       x = 60      x = 117.5

y = 55                        y = 60           y =62.5
15. Use the drawing to find the measure of   20. Archaeologist Eartha Diggs has uncovered a
1, 2 and 3. m1  3x  3, m2  y ,       piece of ceramic plate. The original plate
m3  7x  15                                appears to have been in the shape of a
regular polygon. If the original plate was a
regular 16-gon, it was probably a ceremonial
1                          dish from the 3rd Century Ho Ping dynasty.
2
If it was a regular 18-gon, it was probably a
3                          palace dinner plate from the 12th century
Wai Ting dynasty. Eartha measures each of
the sides of her piece and finds that they are
all the same size. She conjectures that all
X=3                                              the sides of the original whole plate were
Angle 1 = angle 3 = 6°                           the same size. She measures each of the
angles on the piece and finds that they are
Angle 2 = 174°                                   all the same size. She conjectures that all
the angles on the original whole plate were
equal. If each angle measures         , what
dynasty did the plate most likely come from?

Exterior = 180-160 = 20
Find the number of sides given the measure
of an exterior angle of a regular polygon.
N = 360/20 = 18
16. Measure of an exterior angle is 72
Therefore, Eartha’s plate
N=5                                               was from the 12th century
Wai Ting dynasty.

17. Measure of an exterior angle is 40.

N=9

Find the number of sides given the measure
of an interior angle of a regular polygon.

18. Measure of an interior angle is 144

N = 10

19. Measure of an interior angle is 150

N = 12

```
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