Question

ln and oq are parallel lines.
which angles are vertical angles?
∠qpr and ∠qpm
∠qpr and ∠lmp
∠qpr and ∠nmk
∠qpr and ∠opm

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines.

Step2: Analyze each option

• For $\angle QPR$ and $\angle QPM$: They are adjacent angles (share a common side $QP$), so they are not vertical angles.
• For $\angle QPR$ and $\angle LMP$: They are not formed by the intersection of the same two lines.
• For $\angle QPR$ and $\angle NMK$: They are not formed by the intersection of the same two lines.
• For $\angle QPR$ and $\angle OPM$: Lines $RK$ and $OQ$ intersect at point $P$. $\angle QPR$ and $\angle OPM$ are non - adjacent angles formed by the intersection of lines $RK$ and $OQ$.

Answer:

$\angle QPR$ and $\angle OPM$