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denis23 [38]
3 years ago
8

Please help Find the measure of UT 65° 51° 70° 55°

Mathematics
1 answer:
Maslowich3 years ago
8 0

\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 \dfrac{\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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