Question 1

Please help Find the measure of UT

65°

51°

70°

55°

Question 2

$\huge\boxed{55^\circ}$

First of all, we know that
$\angle Q=95^(\circ)$ because of its vertical angle.
$\angle Q$ is also equal to
$\frac{\widehat{RS}+\widehat{UT}}{2}$ because it's an interior angle.

$\begin{aligned}\angle Q&=\frac{\widehat{RS}+\widehat{UT}}{2}\\95^\circ&=\frac{135^\circ+\widehat{UT}}{2}&&\qquad&&\textsf{Substitute in the known values.}\\190^\circ&=135^\circ+\widehat{UT}&&\qquad&&\textsf{Multiply both sides by $2$.}\\55^\circ&=\widehat{UT}&&\qquad&&\textsf{Subtract $135^\circ$ from both sides.}\\\widehat{UT}&=\boxed{55^\circ}&&\qquad&&\textsf{Switch the sides of the equation to show our answer.}\end{aligned}$

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