Notice that, since X and Y are the midpoints of UV and UW, respectively,
[tex]\frac{XU}{UV}=\frac{UY}{UW}=\frac{1}{2}[/tex]
and triangles XUY and VUW share angle Two corresponding angles of a pair of similar triangles are congruent; thus
[tex]\begin{gathered} \Rightarrow\angle UYX\cong\angle W \\ \Rightarrow\angle W=42 \end{gathered}[/tex]
The answer is
