Question

the exterior angle of a regular polygon is one third of its interior angle.find the no. of sides in polygon

Answer 1

Let the interior angle be x then exterior angle = 3x

So x+3x=360

x=90

The only regular polygon (in a regular polygon all angles are equal) that has all angles 90 is square or rectangle.... So its a polygon with 4 sides

Answer 2

sum of int. angle = (2n-4)×90
sum of all int. angle of polygon=3( sum of int. angle)
(2n-4)90=3×360
(2n-4)=3×360/90
(2n-4)=3×4
2n=12+4
n=16/2
n=8