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

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.