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

Question

campbell_st · Answer

well the exterior angles of any polygon sum to 360 

so you can find the number of sides/angles in the polygon by dividing 360 by the known exterior angle. 

360/30 = 12

so the polygon has 12 sides

the sum of the interior angles is found using the formula 

$$A = 180 \times (n - 2)$$

where n is the number of sides. 

hope this helps.