Question

The number of sides of a regular polygon whose exterior and interior angles are in the ratio 1 : 5 is ___

Answer 1

Let the number of sides of polygon = n
Each exterior angle $=x^{\circ }$
Each interior angle $=5x^{\circ }$
Sum of one interior angle and the corresponding exterior angle is ${180}^{\circ }$
$\therefore$ $x+5x={180}^{\circ }$
$x=\frac{{180}^{\circ }}{6}={30}^{\circ }$
Sum of all exterior angles $=(360{)}^{\circ }$
If the polygon is regular, then each exterior angle measures $\frac{{360}^{\circ }}{n}$.
$\Rightarrow {30}^{\circ }\times n={360}^{\circ }$
$\Rightarrow n=\frac{{360}^{\circ }}{{30}^{\circ }}$
Hence, n = 12.