Question

ln and oq are parallel lines. which angles are alternate interior angles? ∠nmp and ∠opm ∠nmp and ∠qpr ∠nmp and ∠nmk ∠nmp and ∠opr

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are formed when a transversal intersects two parallel lines. They lie between the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each option

• For $\angle NMP$ and $\angle OPM$:

Since $\overline{LN}\parallel\overline{OQ}$ and $\overline{RK}$ is the transversal. $\angle NMP$ and $\angle OPM$ lie between $\overline{LN}$ and $\overline{OQ}$ and on opposite sides of $\overline{RK}$.

• For $\angle NMP$ and $\angle QPR$: $\angle QPR$ is not between the two parallel lines $\overline{LN}$ and $\overline{OQ}$.
• For $\angle NMP$ and $\angle NMK$: $\angle NMK$ is not on the opposite side of the transversal with respect to $\angle NMP$ in the context of the two parallel lines.
• For $\angle NMP$ and $\angle OPR$: $\angle OPR$ is not between the two parallel lines $\overline{LN}$ and $\overline{OQ}$.

Answer:

$\angle NMP$ and $\angle OPM$