Question

What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 30°?

Answer 1

The sum of the exterior angles, one per vertex, of a regular polygon is 360. Because the polygon is regular, the interior angles are congruent causing the exterior angles also to be congruent.

360/30 = 12 which is the number of sides of the regular n-gon which we now know is a dodecagon.

The sum of the interior angles (12-2) 180 = 1800.

Alternatively, each interior angle has measure 150 as it forms a linear pair with its adjacent exterior angle. 150 * 12 = 1800.