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