Question

look at this diagram: if $overleftrightarrow{mo}$ and $overleftrightarrow{pr}$ are parallel lines and $mangle pqn = 137^{circ}$, what is $mangle onq?$

Explanation:

Step1: Identify angle - relationship

$\angle PQN$ and $\angle ONQ$ 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 lines and $\angle PQN = 137^{\circ}$, then $m\angle ONQ=m\angle PQN$.

Answer:

$137$