Question

The rario between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find :

(i) each exterior angle of the polygon ;

(ii) number of sides in the polygon.

Answer 1

Interior angle : exterior angle = 2 : 1

$\therefore$ Let interior angle $=2x^o$

& exterior angle $=x^o$

$\therefore 2x^o+x^o={180}^{o}3x={180}^o$

(i) $x={60}^o$

$\therefore$ Each exterior angle $={60}^o$

Let No. of sides = n

$\therefore \frac{{360}^o}{n}={60}^{o}n=\frac{{360}^o}{{60}^o}$

(ii) n = 6

$\therefore \left(i\right){60}^o\left(ii\right)6$.