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

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) (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

When the polygon is regular, all of its angles are equal so to find the measure of one interior angle, we divide by n:

Solving, we have --> 5n = 360 --> n = 72. This is an integer, so a regular polygon with 72 sides would have interior angles measuring 175 degrees.
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