Geometry

The formula for # of diagonals for a n-sided poligon is $\frac{n (n - 3)}{2}$. Therefore,

$\frac{n(n-3)}{2} = 2n$

$n^2 - 3n = 4n$

$n^2-7n=0$

$n(n-7)=0$

$n = 0, 7$

And since there are no 0-sided polygons, the polygon has 7 sides