Question

sum of the interior angles of polygon is 8 times the sum of its exterior angles then the number of sides of the polygon is

Answer 1

(1) Sum of interior angles
= (2n– 4) × 90
Now, Sum of interior angles of a polygon
= 8(Sum of interior angles)      
(2n – 4) 90 = 8× 360
(2n – 4) = 8× 4
2n=32+4
2n=36
n=18

so number if sides is 18

Answer 2

Step-by-step explanation:

The sum of the internal angles of a polygon is = 180o(n−2)

Sum of exterior angle of a polygon is = 360o

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

Then, 

 180o(n−2)=8×360o

=>n−2=16

=>n=18 

Number of sides of polygon is 18.