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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

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daijingyi722
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.

TheBlueFox

The polygon would have 24 sides.

[tex]\frac{180n -  360}{n}[/tex] ≈ [tex]\frac{360}{n}[/tex] ([tex]\frac{11}{1}[/tex])

[tex]\frac{180n -  360}{n}[/tex] = [tex]\frac{3960}{n}[/tex]

180n - 360 = 3,960

180n = 4,320

n = 24

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