Question

Find the missing angle measure.128 °38 °?VX

Answer 1

QRST is a parallelogram, so:

`\begin{gathered} SR\parallel TQ \\ SR\cong TQ \end{gathered}`

This means that, by Alternate interior Angles:

`\begin{gathered} m\angle SRT\cong m\angle RTQ \\ m\angle RSQ\cong m\angle SQT \end{gathered}`

By Vertical Angles:

`m\angle SUR\cong m\angle TUQ`

Thus, Triangles SUR and TUQ are congruent. This means that:

`RU=UT`

So,

`\begin{gathered} RT=UT+RU=UT+UT=2UT \\ 2UT=44 \\ UT=22 \end{gathered}`

Answer: UT = 22.