SOLUTION: What is the measure of each interior angle of a regular convex 72-gon?

The sum of the interior angles of any polygon with n sides is


In this case n = 72, so we substitute


 




Since the polygon is regular, all 72 interior angles are
equal in measure, so we divide by 72 to find what each
interior angle measures:



Ever seen a regular 72-gon?  Here's one. Notice that it looks
almost like a circle, but if you look carefully, you'll see
that the sides are straight.   [Some look jagged but that's
because of the pixels on your screen].



Edwin