Question

X is the midpoint of UV. Y is the midpoint of UW. If m∠UYX=42, find m∠W.m∠W.=

Answer 1

Notice that, since X and Y are the midpoints of UV and UW, respectively,

$\frac{XU}{UV}=\frac{UY}{UW}=\frac{1}{2}$

and triangles XUY and VUW share angle Two corresponding angles of a pair of similar triangles are congruent; thus

$\begin{gathered} \Rightarrow\angle UYX\cong\angle W \\ \Rightarrow\angle W=42 \end{gathered}$

The answer is