Question

The measure of each interior angle of a regular polygon is eleven times that of an exterior angle how many sides does the polygon have

Answer 1

let there be x sides.
180(x-2)/x=11*360/x
180(x-2)=11*360
x-2=11*2
x-2=22
x=24

the polygon has 24 sides.

Answer 2

The polygon would have 24 sides.

`(180n -  360)/(n)` ≈
`(360)/(n)` (
`(11)/(1)`)

`(180n -  360)/(n)` =
`(3960)/(n)`

180n - 360 = 3,960

180n = 4,320

n = 24