Question

The measure of an exterior angle of a regular polygon is 24. Find the measure of an interior angle. Then find the number of sides.

Answer 1

Interior and exterior angles are supplementary, so the interior angle has measure

$24^\circ+x^\circ=180^\circ\implies x=156$

The exterior angles of a convex polygon all add up to $360^\circ$, and in a regular polygon these angles are all congruent. So if there are $n$ sides, you have

$24^\circ n=360^\circ\implies n=15$