SOLUTION: Each interior angle of a regular polygon is thrice each exterior angle. Find the number of side of the polygon.

An interior angle and an exterior angle at a vertex of a polygon
are supplementary.

Let the exterior angle be X.
Then the interior angle is 3X.
Since they are supplementary,

X + 3X = 180°
    4X = 180°
     X = 45°

So each exterior angle is 45°, and each interior angle is 3×45°=135°.

Let the number of sides be N.

The sum of the exterior angles of a polygon is 360°

Since the polygon is regular, each interior angle is 
So



Multiply both sides by N



Divide both sides by 45°



It's an 8-sided regular polygon, a regular octagon.
In the regular octagon below, the 135° angle is an INTERIOR angle,
and the 45° angle is an exterior angle.  



Edwin