Interior and external angles of a polygon

Hi my name is anthony, the level is middle, and i am a student.

Yes I have another question to help me study for a math exam coming up on january 30.

This time the question is about finding interior and/or exterior angles.

the question is:

In a regular polygon, the ratio of the interior angles to the exterior angles is 3:1.

(a) Find the measure of the interior angle.
(b) How many sides are there

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