Pentagon $FGHIJ$ is similar to pentagon $VWXYZ$, where $F,G,H,I,$ and $J$ correspond to $V,W,X,Y,$ and $Z$, respectively. The measure of angle $G$ is $110^{\circ }$. The perimeter of pentagon $VWXYZ$ is 4 times the perimeter of pentagon $FGHIJ$. What is the measure of angle $W$?