SOLUTION: is it possible for a regular polygon to have an interior angle that measures 175 degree? why or why not?

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Question 377945: is it possible for a regular polygon to have an interior angle that measures 175 degree? why or why not?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that the formula for the sum of the measures in a convex polygon with n sides is
S+=+180%28n-2%29
When the polygon is regular, all of its angles are equal so to find the measure of one interior angle, we divide by n:
175+=+180%28n-2%29%2Fn
Solving, we have 175n+=+180n+-+360 --> 5n = 360 --> n = 72. This is an integer, so a regular polygon with 72 sides would have interior angles measuring 175 degrees.