In a similar configuration of three intersecting lines at point P, the adjacent angles $x^{\circ }$, $y^{\circ }$, and $z^{\circ }$ lie on a straight line, and the angle between $y^{\circ }$ and $z^{\circ }$ is vertical to $x^{\circ }$. If $x=40$ and $y=55$, find $z$.