Question

look at this diagram: if $overleftrightarrow{ln}$ and $overleftrightarrow{oq}$ are parallel lines and $mangle opr = 61^{circ}$, what is $mangle lmp$?

Explanation:

Step1: Identify angle - type relationship

$\angle OPR$ and $\angle LMP$ are alternate - interior angles.

Step2: Apply alternate - interior angles property

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since $\overleftrightarrow{LN}$ and $\overleftrightarrow{OQ}$ are parallel and $RK$ is the transversal, $m\angle LMP=m\angle OPR$.

Answer:

$61$