SOLUTION: What is the formula to find out the number of sides of a regular polygon when one interior angle is given?

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Question 251990: What is the formula to find out the number of sides of a regular polygon when one interior angle is given?

Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
(n-2)180=sum of the interior angles. If you just want to find one angle, then you divide (n-2)180 by the number of sides and you get
%28%28%28n-2%29180%29%2Fn%29 = one angle of a regular polygon
since you know the angle, you set the angle equal to %28%28n-2%29180%29%2Fn%29
Let the angle be represented by A.
%28%28n-2%29180%29%2Fn%29=A using algebra, we can say
%28n-2%29180=An
180n-360-An=0
180n-An=360
n(180-A)=360
n=360/(180-A)
Therefore, the formula to find out the number of sides of a regular polygon when one interior angle is given is:
n=360%2F%28180-A%29
Where n=number of sides and A is the given angle.
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