Question

ln and oq are parallel lines. which angles are vertical angles? ∠opm and ∠qpm ∠lmk and ∠nmp ∠nmk and ∠qpm ∠opr and ∠nmp

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. They are opposite each other and are equal in measure.

Step2: Analyze each option

• For $\angle OPM$ and $\angle QPM$: These are adjacent angles (they share a common side $PM$ and a common vertex $P$), so they are not vertical angles.
• For $\angle LMK$ and $\angle NMP$: These are vertical angles. They are formed by the intersection of lines $LN$ and $RK$ at point $M$. They are non - adjacent and opposite each other.
• For $\angle NMK$ and $\angle QPM$: These angles are not formed by the intersection of the same two lines, so they are not vertical angles.
• For $\angle OPR$ and $\angle NMP$: These angles are not formed by the intersection of the same two lines, so they are not vertical angles.

Answer:

$\angle LMK$ and $\angle NMP$