QRST is a parallelogram, so:
[tex]\begin{gathered} SR\parallel TQ \\ SR\cong TQ \end{gathered}[/tex]This means that, by Alternate interior Angles:
[tex]\begin{gathered} m\angle SRT\cong m\angle RTQ \\ m\angle RSQ\cong m\angle SQT \end{gathered}[/tex]By Vertical Angles:
[tex]m\angle SUR\cong m\angle TUQ[/tex]Thus, Triangles SUR and TUQ are congruent. This means that:
[tex]RU=UT[/tex]So,
[tex]\begin{gathered} RT=UT+RU=UT+UT=2UT \\ 2UT=44 \\ UT=22 \end{gathered}[/tex]Answer: UT = 22.
