Question

the exterior angle of a regular polygon is one third of its interior angle find the number of sides in the polygon

Answer 1

Given that exterior angle of a regular polygon is 1/3rd of its interior angle.

We know that measure of an interior angle = (n-2)(180/n) and the measure of an exterior angle = (360/n).

1/3 = (360/n)  / (n-2)(180/n)

1/3 = (360/n) / n/(n - 2) * 180

1/3 = (360/n) / n(180n - 360)

1/3 = (360)/(180(n-2))

1/3 = 2/(n-2)

1(n - 2) = 3 * 2

n - 2 = 6

n = 2 + 6

n = 8.

Therefore the number of sides in the polygon = 8.


Hope this helps!