Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle utv = 138^{circ}$, what is $mangle rqt$?

Explanation:

Step1: Identify angle - relationship

$\angle UTV$ and $\angle RQT$ are corresponding angles.

Step2: Apply property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are congruent. So $m\angle RQT=m\angle UTV$.

Answer:

$138$