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.

$\frac{180n - 360}{n}$ ≈ $\frac{360}{n}$ ($\frac{11}{1}$)

$\frac{180n - 360}{n}$ = $\frac{3960}{n}$

180n - 360 = 3,960

180n = 4,320

n = 24