SOLUTION: A regular polygon has an interior angle that measures 144 degrees, and a side of which is 12 units long. What is the perimeter of the regular polygon?

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Question 252457: A regular polygon has an interior angle that measures 144 degrees, and a side of
which is 12 units long. What is the perimeter of the regular polygon?
Found 2 solutions by Earlsdon, richwmiller:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to find the number of sides in the regular polygon.
You are given the measure of an interior angle (144 degrees) from which you can find the number of sides.
The interior angle (144 degrees in this case) of a regular polygon of n sides is given by:
%28n-2%29%2A180%2Fn+=+144
%28n-2%29%2A180+=+144n
180n-360+=+144n
180n+=+144n%2B360
36n+=+360
highlight_green%28n+=+10%29
The regular polygon has 10 sides and its perimeter (P) is:
P+=+10%2812%29
highlight%28P+=+120%29units.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
n= number of sides
sum of angles=180(n-2)
180(n-2)/n=144
n=10
10*12=120 units