Triangle $ABC$ is similar to triangle $XYZ$, where $A,B,$ and $C$ correspond to $X,Y,$ and $Z$, respectively. The measure of angle $A$ is $45^{\circ }$ and the measure of angle $B$ is $60^{\circ }$. The sides of triangle $XYZ$ are $\frac{1}{2}$ the length of the corresponding sides of triangle $ABC$. What is the measure of angle $X$?