Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle utq = 136^{circ}$, what is $mangle pqt$?

Explanation:

Step1: Identify angle - relationship

$\angle UTQ$ and $\angle PQT$ are same - side interior angles.

Step2: Recall property of same - side interior angles

For parallel lines $\overleftrightarrow{PR}$ and $\overleftrightarrow{SU}$, same - side interior angles are supplementary, i.e., $\angle UTQ+\angle PQT = 180^{\circ}$.

Step3: Solve for $\angle PQT$

Given $\angle UTQ = 136^{\circ}$, then $\angle PQT=180^{\circ}-\angle UTQ$. So, $\angle PQT = 180 - 136=44^{\circ}$.

Answer:

$44$