SOLUTION: One exterior angle of a regular polygon measures 24 degrees. What is the sum of the measures of the interior angles of the polygon? Thanks for your help.

Question 311308: One exterior angle of a regular polygon measures 24 degrees. What is the sum of the measures of the interior angles of the polygon?
Thanks for your help.

Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Since the measure of the exterior angle of a regular polygon is 360/n, where n is the number of sides, we have
360/n = 24 and
n = 15 sides.
The total number of degrees in the interior of a polygon of n sides is
180(n-2) = 180(15-2) = 180(13) = 2340 degrees total.
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