Elementary Geometry for College Students (6th Edition)

$m\angle W=92^{\circ}$
Given that the two triangles are similar, then their corresponding angles are congruent. Thus... $m\angle R=m\angle U=67^{\circ}$ and $m\angle S=m\angle V=21^{\circ}$ The sum of the interior angles of a triangle is $180^{\circ}$... $180-67-21=92$ $m\angle W=92^{\circ}$