Question 1011166
E = exterior angle
I = interior angle


I = 8*E since the "interior angle is 8 times as large as its exterior angle"


Each pair of interior and exterior angles add up to 180 degrees
E + I = 180 degrees
E + 8*E = 180 ... replace I with 8E; solve for E
9E = 180
E = 180/9
E = 20


Each exterior angle is 20 degrees


Now let n = number of sides. We can tie n and E together with this formula


E = 360/n


Solve for n to get n = 360/E. Now plug in E = 20


n = 360/E
n = 360/20
n = 18


So there are 18 sides of this polygon.