Question

Select which type of polygon this figure is, and find the measures of the indicated interior and exterior angles.

A. regular octagon; interior: 135; exterior: 45
b. regular octagon; interior: 140; exterior: 40
c. regular decagon; interior: 140; exterior: 40
d. regular decagon; interior: 144; exterior: 36
e. regular nonagon; interior: 144; exterior: 36

Answer 1

d. regular decagon; interior: 144; exterior: 36

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Answer 2

Answer: D

Explanation:

It has 10 sides. It is a decagon.

The value of the interior angles (total when all are added together) is

(n - 2)*180

(10 - 2)* 180

8 * 180 = 1440

But a regular decagon has 10 angles (as well as 10 sides).

1440/10 = 144

So each interior angle is 144 degrees.

The exterior angles are the supplement of the interior angles. (They also must add to 360 no matter how many interior angles there are).

144 + x = 180

x = 180-144

x = 36 degrees.