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

Given ⇒
Ratio of the Exterior angle to an Interior angle of a Regular Polygon is 2:3.

We know, 
Exterior angle of the Regular Polygon = 360°/n
where, n is the number of the sides in the polygon.

Interior angle of the Regular Polygon = (n - 2) × 180/n

Now, Substituting these values in the ratio,

 (360°/n) ÷ [(n - 2)180]/n = 2/3
⇒ 360/(n - 2)180 = 2/3
⇒ 2/(n - 2) = 2/3
∴ n - 2 = 3
∴ n = 3 + 2
∴ n = 5 sides.


Hence, the number of the sides in the Regular Polygon is 5.


Hope it helps.