Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle stq = 42^{circ}$, what is $mangle rqt?$

Explanation:

Step1: Identify angle - relationship

$\angle STQ$ and $\angle RQT$ are alternate - interior angles.

Step2: Apply property of parallel lines

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. So $m\angle RQT=m\angle STQ$.

Answer:

$42$