Hi Anthony,
I drew three consecutive vertices O, P and Q of the polygon and extended the line OP to a point S.
The interior angle OPQ is 3 times as large as the external angle QPS and the sum of these two angles is 180^{o}. Hence 4 time the angle QPS is 180^{o} and thus angle QPS is 45^{o}. Now can you tell how many sides there are?
Penny
