Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle utq = 43^{circ}$, what is $mangle pqt$?

Explanation:

Step1: Identify angle - relationship

$\angle UTQ$ and $\angle PQT$ 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 $\overleftrightarrow{PR}$ and $\overleftrightarrow{SU}$ are parallel and $VO$ is the transversal, $m\angle UTQ=m\angle PQT$.

Answer:

$43^{\circ}$