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.

+2

(1) Answers

jackie1977

Interior and exterior angles are supplementary, so the interior angle has measure
[latex]24^\circ+x^\circ=180^\circ\implies x=156[/latex]
The exterior angles of a convex polygon all add up to [latex]360^\circ[/latex], and in a regular polygon these angles are all congruent. So if there are [latex]n[/latex] sides, you have
[latex]24^\circ n=360^\circ\implies n=15[/latex]