In the figure shown, lines $k$ and $l$ are parallel, and line $m$ is a transversal. If the measure of angle $A$ is $(4x-10{)}^{\circ }$ and the measure of angle $B$ is $(2x+30{)}^{\circ }$, and angle $A$ and angle $B$ are alternate interior angles, what is the value of $x$?

Note: Figure not drawn to scale.