+135 \(\angle{P} = \angle{TUV}\)
\(\angle{PUV} = \angle{UTR}\)
\(\angle{PQV} = \angle{UVR}\)
\(\angle{QVU} = \angle{VRT}\)
Therefore, trapezoid PUVQ is similar to trapezoid UTRV
\(\overline{TR} = \frac{2}{7}(20) = \frac{40}{7}\)
Since \(PUVQ \sim UTRV\):
\(\frac{20}{UV} = \frac{UV}{\frac{40}{7}}\)
\(\frac{800}{7} = \overline{UV}^2\)
\(\textbf{UV = }\frac{\textbf{20}\sqrt{\textbf{2}}}{\sqrt{\textbf{7}}}\)
\(\textbf{UV = }\frac{\textbf{20}\sqrt{\textbf{14}}}{{\textbf{7}}}\)
Let me know if I made any mistakes!
