Question

select all the pairs of vertical angles.
∠mnl and ∠onq
∠onl and ∠rqs
∠onl and ∠mnl
∠pqn and ∠rqs

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are the opposite angles formed by the intersection of two lines. They are equal in measure and share a common vertex, with their sides being opposite rays.

Step2: Analyze each pair

• For $\angle MNL$ and $\angle ONQ$: Lines $MO$ and $SL$ intersect at $N$, so these are vertical angles.
• For $\angle ONL$ and $\angle RQS$: $\angle ONL$ and $\angle RQS$ do not satisfy the vertical angle definition (different intersections), so this is incorrect.
• For $\angle ONL$ and $\angle MNL$: These are adjacent angles, not vertical angles (they share a common side), so this is incorrect.
• For $\angle PQN$ and $\angle RQS$: Lines $PR$ and $SL$ intersect at $Q$, so these are vertical angles.

Answer:

The correct pairs of vertical angles are:

• $\angle MNL$ and $\angle ONQ$
• $\angle PQN$ and $\angle RQS$