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

The ratio between the exterior angle and interior angle of a regular polygon is 2:3.
Each interior angle of a regular polygon $=\frac{180(n-2)}{n}$
Where n = number of sides of polygon
Each exterior angle of a regular polygon $=\frac{360}{n}$
According to question,
$\frac{360}{n}:\frac{180(n-2)}{n}=2:3\frac{2}{(n-2)}=\frac{2}{3}$
n-2 = 3
n = 5