Question

If the ratio of the interior angle to the exterior angle is 5:1 for a regular polygon, find
a. the size of each exterior angle
b. the number of sides of the polygon
c. the sum of the interior angles
d. Name the polygon

Answer 1

interior: (n-2)180/n
exterior: 360/n

(n-2)180/n ÷ 360/n = (n-2)/2 = 5
n = 8

a:
exterior: 45
interior: 135

b: n=8

c: 6(180) = 1080

d: octagon

Answer 2

Oops
n=12

exterior: 30
interior: 150

n=12

10(180) = 1800

dodecagon

Answer 3

The ratio of interior and exterior angle of regular polygon is is 5:1, find the number of diagonals of the regular polygon.