Question

The sum of the interior angles of a polygon is three times the sum of its exterior angle. Find the number of sides of the polygon

Answer 1

As we know that sum of exterior angles of a polygon is always 360°.
And, Sum of interior angles is given 360°*3= 1080°.
Sum of interior angles = (n-2)*180°=1080°
i.e. n= 8 sides.

Answer 2

Given that,

The sum of the interior angles of a polygon is three times the sum of its exterior angle.

To find,

The number of sides of the polygon.

Solution,

We know that,

The sum of interior angles of a polygon = 180(n-2), n = no of sides

The sum of exterior angles of a polygon = 360

ATQ,

180(n-2)=3(360)

180n-360=1080

180n=1080+360

180n = 1440

⇒ n = 8

So, there are 8 sides of the polygon.