Find the sum of the interior angles of the polygon

Question

The measure of an exterior angle of a regular polygon is 7.5. What is the sum of the interior angles of the polygon?

Answer 1

The sum of the exterior angles of a polygon is 360, so there are 360/7.5 = 48 sides to the polygon.

The sum of the interior angles of a polygon are (n-2)180, where n is the number of sides, so for a 48-sided polygon, that sum is (48-2) 180 = 46 * 180 = 8280.