Question

The measure of each interior angle of a regular polygon is five times the measure of its interior angle. Find:
(i) measure of each interior angle,
(ii) measure of each exterior angle and
(iii)number of sides in the polygon

Answer 1

1)Let x be interior angle of the polygon,then
x=5(180-x)
x=5×180-5x
6x=900
x=900/6=150°

2)
Exterior angle=180-x
=180-150
=30°
3)
number of sides of polygon=360/30
=12