Question

look at this diagram: if $overleftrightarrow{mo}$ and $overleftrightarrow{pr}$ are parallel lines and $mangle pqs = 65^{circ}$, what is $mangle mnq$?

Explanation:

Step1: Identify angle - relationship

$\angle PQS$ and $\angle MNQ$ 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 $\overleftrightarrow{MO}$ and $\overleftrightarrow{PR}$ are parallel and $SL$ is the transversal, $m\angle MNQ=m\angle PQS$.

Answer:

$65$