Question

The exterior angle of a regular polygon is one-third of its interior angle.How many sides does the polygon has ?

Answer 1

Answer:

Step-by-step explanation:

The exterior angle of a regular polygon is one-third of its interior angle. How many sides does the polygon have?

Sum of exterior and interior angles is 180 deg.

If the interior angle is 3x, the exterior angle is x. Hence 3x+x = 4x = 180 or x = 45. The interior angle is 135 deg. So the polygon has 360/45 = 8 sides or it is a regular octagon.

Answer 2

let the interior angle be x . then the exterior angle is x/3.
x+x/3 = 360
4x/3=360
4x=3×360
x=270°
then interior angle is 360-270=90°
sum of all the exterior angles of a polygon=360°
therefore no:of sides=360/90=4