Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle pqt = 50^{circ}$, what is $mangle utq?$

Explanation:

Step1: Identify angle - relationship

$\angle PQT$ and $\angle UTQ$ are alternate - interior angles.

Step2: Apply property of alternate - interior angles

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since $\overleftrightarrow{PR}\parallel\overleftrightarrow{SU}$ and $OV$ is the transversal, $m\angle PQT=m\angle UTQ$.

Answer:

$50$