Question

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :

(i) measure of each interior angle :

(ii) measure of each exterior angle and

(iii) number of sides in the polygon.

Answer 1

Let exterior angle = $x^o$

$\therefore$ Interior angle $=5x^o$

$\therefore x+5x={180}^{o}6x={180}^{o}x={30}^o$

$\therefore$ Each exterior angle $={30}^o$

Each interior angle $=5\times {30}^o={150}^o$

Let no. of sides = n

$\because$ each exterior angle $=\frac{{360}^o}{n}{30}^o=\frac{{360}^o}{n}n=\frac{{360}^o}{{30}^o}n=12$

Hence (i) ${150}^o$ (ii) ${30}^o$ (iii) 12.