If the ratio of the interior angle to the exterior angle is 5:1 for a regular polygon, find

Question

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.