Question

The measure of an exterior angle of a regular polygon is 15°. What is the sum of the measures of the interior angles of the polygon?

Answer 1

First thing you must do is find the number of sides of the polygon.
The sum of all the exterior angles of a polygon is always 360°.
360/15 = 24
The polygon has 24 sides.

The formula for the sum of the interior angles of a polygon is:
180(n - 2)
Where n is the number of sides.

180(24 - 2)
180(22)
3960

The sum of the measure of the interior angles of the polygon is 3960.