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:
[tex]\begin{gathered} m\angle T+m\angle U=180\degree \\ \implies(2x-9)+5x=180\degree \end{gathered}[/tex]
First, solve the equation for x:
[tex]\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} \\ \frac{7x}{7}=\frac{189}{7} \\ x=27\degree \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} m\angle T=2x-9 \\ =2(27)-9 \\ =54-9 \\ =45\degree \end{gathered}[/tex]
The measure of angle T is 45 degrees.
