Question

the sum of interior angles of a polygon is three times the sum of its exterior angles. Then number of sides in the polygon is

Answer 1

Sum of interior angles =3x360 =1080

Now! Let the no. Of sides be n
So, (n-2)x180°=1080°
n=(1080/180)+2
n=6+2
n=8

The polygon is an octagon

Answer 2

Sum of exterior angles = 360

Sum of interior angles = 3 x 360 = 1080

.

Sum of interior angles = (n - 2) x 180 where n is the number of sides

(n - 2) 180 = 1080

.

Solve n:

(n - 2) 180 = 1080

180n - 360 = 1080

180n = 1440

n = 1440 ÷ 180 = 8 sides

.

Answer: There are 8 sides in this polygon.