Question

Is it possible to have a regular polygon whose each exterior angle is :

(i) ${80}^o$

(ii) $40\%$ of a right angle.

Answer 1

(i) Let no. of sides = n

each exterior angle $={80}^o$

$\therefore \frac{{360}^o}{n}={80}^{o}n=\frac{{360}^o}{{80}^o}\therefore n=\frac{9}{2}$

Which is not a whole number.

Hence it is not possible to have a regular polygon whose each exterior angle is of ${80}^o$.

(ii) Let number of sides = n

Each exterior angle = 40 % of a right angle

$=\frac{40}{100}\times 90={36}^{o}n=\frac{{360}^o}{{36}^o}n=10$

Which is a whole number.

Hence it is possible to have a regular polygon whose each exterior angle is $40\%$ of a right angle.