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°

Interior angle = 5x°

x + 5x = 180°

6x = 180°

x = 30°

Each exterior angle = 30°

Each interior angle = 5 x 30° = 150°

Let no. of sides = n

∵ each exterior angle = `360^circ/"n"`

`30^circ = (360^circ)/"n"`

n = `(360^circ)/30^circ`

n = 12

Hence (i) 150° (ii) 30° (iii) 12