Question

What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 72°?

Answer 1

The sum of interior and exterior angle is 180, thusInterior angle =180−72=108 degrees Let n be the number of sides of the polygon(n−2)×180 / n = interior angle =10872n = 360 n = 5 sides, hence this is a pentagon. 
Sum of the interior angles = 108*5 = 540 degrees.