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I am trying to find the measure of angle T

I am trying to find the measure of angle T-example-1

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Answer:

m∠T= 45°

Explanation:

In a parallelogram, consecutive (or adjacent) angles add up to 180 degrees.

In parallelogram MNTU, angles T and U are consecutive angles, therefore:


\begin{gathered} m\angle T+m\angle U=180\degree \\ \implies(2x-9)+5x=180\degree \end{gathered}

First, solve the equation for x:


\begin{gathered} 2x-9+5x=180\degree \\ \text{ Add 9 to both sides of the equation} \\ 2x-9+9+5x=180\operatorname{\degree}+9 \\ 7x=189 \\ \text{ Divide both sides by 7} \\ (7x)/(7)=(189)/(7) \\ x=27\degree \end{gathered}

Therefore:


\begin{gathered} m\angle T=2x-9 \\ =2(27)-9 \\ =54-9 \\ =45\degree \end{gathered}

The measure of angle T is 45 degrees.

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