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

The sum of interior and exterior angle is 180, thus Interior angle = 180-72=108 degrees Let n be the number of sides of the polygon (n-2) * 180 / n = interior angle = 108 72n = 360 n = 5 sides, hence this is a pentagon.

Sum of the interior angles = 108*5 = 540 degrees.