Question

The size of each interior angle of a regular polygon is 8 times the sizes of each exterior angle.

work out how many sides the polygon has.
let the size of each exterior angle be x degrees in your working

Answer 1

18 sides

Explanation:

Exterior angle: x = 360/n

Interior angle: 8x = (n-2)×180/n

(n-2)×180/n = 8 × 360/n

n - 2 = 16

n = 18

Answer 2

20

Explanation:

To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides or angles that the polygon has. For example, an eight-sided regular polygon, an octagon, has exterior angles that are 45 degrees each, because 360/8 = 45.

If each interior angle is 8 times the degree measure of each exterior angle how many sides does the polygon have. Now 8+1 = 9. Divide 180 by 9 to get 20.