Question

which angles are alternate interior angles? ∠lmp and ∠qpm ∠lmp and ∠opr ∠qpm and ∠nmk ∠nmp and ∠qpm

Explanation:

Step1: Recall alternate - interior angles definition

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

Step2: Analyze each option

• For $\angle{LMP}$ and $\angle{QPM}$: They are on the interior of the lines formed by $\overleftrightarrow{LN}$ and $\overleftrightarrow{OQ}$ and on opposite sides of the transversal $\overleftrightarrow{RK}$.
• $\angle{LMP}$ and $\angle{OPR}$ are not alternate - interior angles as they are not in the correct relative position with respect to the lines and transversal.
• $\angle{QPM}$ and $\angle{NMK}$ are not alternate - interior angles.
• $\angle{NMP}$ and $\angle{QPM}$ are adjacent angles, not alternate - interior angles.

Answer:

$\angle{LMP}$ and $\angle{QPM}$