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`