Question

The exterior angle of a regular polygon is one third of its interior angle how many sides has the polygon?​

Answer 1

sum of exterior and interior angle =180

let interior angle = x

exterior = 1/3 x

x + 1x/3 = 180

4x / 3 = 180

x = 180× 3/4

x = 45×3

x = 135

exterior angle = 1/3×135= 45

number of side = 360/45 = 8 sides

360 is taken because sum of exterior angle in any polygon is 360.

Answer 2

Answer:

let interior angle be x

exterior angle=x/3

x+x/3=180°{linear pair}

2x=180°×3

2x=540°

x=540÷2

x=270°

interior angle =270°

exterior angle=270/3=90°

exterior angle sum=360°

no.of sides polygon has=360°÷90°=4

So, polygon has 4 sides..