Question

The ratio between an exterior angle and an interior angle of a regular polygon is 2 : 3. Find the number of sides in the polygon.

Answer 1

Let the measure each interior and exterior angles are 3k and 2k.

Let the number of sides of the polygon is n.

Now we can write:

n.3k = ( 2n − 4 ) × 90°

3nk = ( 2n − 4 ) 90°                  ....(1)

Again

n.2k = 360°

nk = 180°

From (1)

3.180° = ( 2n − 4 ) 90°

3 = n − 2

n = 5

Thus the number of sides of the polygon is 5.