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
\(24^\circ n=360^\circ\implies n=15\)
