Question

each interior angle of a regular polygon is 18 degree more than eight times an exterior angle. the number os sides of polygon is.

Answer 1

at each vertex, interior + exterior = 180 degrees.

If exterior = x,

x+(8x+18) = 180
9x = 162
x = 18

he exterior angle of a regular n-gon is 360/n, so

18 = 360/n
n = 20

Answer 2

Interior angle = 180 - (exterior angle) = 180 -360/N

Exterior angle = 360/N

180 - (360/N) = [8*360/N] +18
9*360/N = 162
N = 20 sides

It is called an icosagon

Answer 3

(2n-4)/n×90
= 8×4×90/n+18
=(2n-4)/n×5= 160/n+1
= 10= n-20=60+n
=10n-n=180
9n=180
n=20