Question

look at this diagram: if $overleftrightarrow{mo}$ and $overleftrightarrow{pr}$ are parallel lines and $mangle pqn = 45.3^{circ}$, what is $mangle mnq?

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Explanation:

Step1: Identify angle - relationship

$\angle PQN$ 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. So $m\angle MNQ=m\angle PQN$.

Answer:

$45.3$