In $△XYZ$ shown, $XY=YZ=10$ and $m\angle Y=120^{\circ }$. If $\overline{YW}$ is an altitude to $\overline{XZ}$, what is the length of $\overline{XZ}$?

(A diagram similar to the original would be provided, showing an isosceles triangle XYZ with altitude YW, where XY=YZ=10 and angle Y = 120 degrees.)