In the figure, line $a$ is parallel to line $b$, and line $c$ is a transversal. An angle formed by line $a$ and line $c$ in the upper-left position measures $(2x+10{)}^{\circ }$. Its consecutive interior angle formed by line $b$ and line $c$ in the lower-left position measures $(3x-20{)}^{\circ }$. What is the value of $x$?