Question

Find the number of sides in a regular polygon, if its each exterior angle is :

(i) $\frac{1}{3}$ of a right angle

(ii) two - fifth of a right - angle.

Answer 1

(i) Each exterior angle $=\frac{1}{3}$ of a right angle

$=\frac{1}{3}\times 90={30}^o$

Let number of sides = n

$\therefore \frac{{360}^o}{n}={30}^o\therefore n=\frac{{360}^o}{{30}^o}n=12$.

(ii) Each exterior angle $=\frac{2}{5}$ of a right - angle

$=\frac{2}{5}\times {90}^o={36}^o$

Let number of sides = n

$\therefore \frac{{360}^o}{n}={36}^{o}n=\frac{{360}^o}{{36}^o}n=10$.