Question

The measure of each exterior angle of a regular polygon is $30$ degrees. What is the sum of the measures of the interior angles, in degrees

Answer 1

Answer: 1800

Explanation:

Exterior angles of a polygon add to 360 degrees, so this means the polygon has 12 sides.

We also know that since an interior angle and its corresponding exterior angle are supplementary, each interior angle is 150 degrees.

Therefore, the sum of the measures of the interior angles is (150)(12)=1800 degrees.