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Please help Find the measure of UT

65°

51°

70°

55°

Please help Find the measure of UT 65° 51° 70° 55°-example-1
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User MtwStark
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1 Answer

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\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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User Kocus
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