In the diagram below, point $U$ is on segment $\overline{BY}$ and the measure of $\angle BUG$ is $30$ degrees greater than the measure of $\angle GUY$: [asy] unitsize(50); pair y=(cos(45*pi/180),sin(45*pi/180)); pair g=(cos(120*pi/180),sin(120*pi/180)); pair b=(cos(225*pi/180),sin(225*pi/180)); pair u=(0,0); dot(y); dot(g); dot(b); dot(u); label("$Y$",y,SE); label("$G$",g,SW); label("$B$",b,SE); label("$U$",u,SE); draw(b--y); draw(u--g); [/asy] How many degrees are in the measure of $\angle GUY$?
