If the measure of the interior angle of a regular polygon is 108
∘
greater than the measure of its exterior angle then how many sides does it have?

Let the measure of the exterior angle be x
∘
.
Then, the measure of the interior angle is (x+108)
∘
.

We know that the sum of an interior angle and an exterior angle of a regular polygon is always 180
∘
:

Interior Angle+Exterior Angle=180
∘

(x+108)+x=180
2x+108=180
2x=72⟹x=36
∘

The exterior angle of the polygon is 36
∘
.

The formula for the number of sides (n) of a regular polygon is:

n=
Exterior Angle
360
∘

​

n=
36
∘

360
∘

​
=10
So, the polygon has 10 sides.