Question

The ratio between exterior angle and interior angle of a regular polygon is 1 : 5. Find the number of sides of the polygon.

Answer 1

Suppose exterior angle of a polygon = x
And interior angle = 5x
$\therefore$ The sum of both exterior and interior angle is 180°.
$\Rightarrow x+5x=180$
$\Rightarrow 6x=180$
$\Rightarrow x=\frac{180}{6}=30°$
$\therefore$ Exterior angle of a polygon = 30°
$\therefore$ The number of sides of the
Polygon $=\frac{{360}^{\circ }}{\text{Exterior angle of a polygon}}$
$=\frac{{360}^{\circ }}{{30}^{\circ }}=12$