Question

How many side does a regular polygon have, whose exterior angle is $8$ times of its interior angle.

Answer 1

Measure of each exterior angle of a polygon$=\frac{360}{n}$

Measure of each interior angle of a polygon$=\frac{(n-2)180}{n}$

$\therefore$ According to question, $\frac{(n-2)\times 180}{n}\times 8=\frac{360}{n}\times 8$

$(n-2)\times 4=16$

$\Rightarrow n=18$

$\therefore$ Sides are $18$.