Question

Question 140
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

Let the exterior angle and interior angle be x and 5x, respectively.
Then, $x+5x={180}^{\circ }$
[$\because$ exterior angle and corresponding interior angle are supplementary]
$\Rightarrow 6x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }}{6}\Rightarrow x=Exteriorangle={30}^{\circ }$
$\therefore$ The number of sides
$=\frac{{360}^{\circ }}{Exteriorangle}$
$=\frac{{360}^{\circ }}{{30}^{\circ }}$
$=12$