Question

select all the pairs of adjacent angles.
∠rqs and ∠pqw ∠pqs and ∠pqw
∠onl and ∠mnl ∠mnl and ∠pqs

Explanation:

Step1: Recall Adjacent Angles Definition

Adjacent angles share a common side and vertex, and their non - common sides are on a straight line (forming a linear pair or not, but sharing side/vertex).

Step2: Analyze Each Pair

• ∠RQS and ∠PQW: Share vertex Q and side QS? Wait, no, re - check. Wait, ∠RQS and ∠PQW: Wait, maybe a typo? Wait, ∠RQS and ∠PQN? Wait, the first pair: Let's look at the lines. Line PR and line SL intersect at Q, line MO and line SL intersect at N. For ∠RQS and ∠PQN: Wait, no, the first option (checked) ∠RQS and ∠PQW? Wait, maybe the correct adjacent pairs:
• ∠RQS and ∠PQN: Wait, no, let's take the pairs:
• ∠RQS and ∠PQN: Wait, actually, ∠RQS and ∠PQN: Wait, no, the first checked pair: ∠RQS and ∠PQW (maybe label error). Wait, the key is adjacent angles share a side and vertex.
• ∠PQ5? Wait, maybe ∠PQS and ∠PQN: They share vertex Q and side QS (wait, no, PQ is common? Wait, maybe the correct pairs are:
• ∠RQS and ∠PQN: Share vertex Q, common side QS? No, maybe ∠RQS and ∠PQW (if W is N). Wait, the checked options: The correct adjacent angle pairs are those that share a common vertex and a common side.
• ∠RQS and ∠PQN: Share Q, and a side.
• ∠PQS and ∠PQN: Share Q and PQ as common side.
• ∠ONL and ∠MNL: Share vertex N and side NL, non - common sides OM and... Wait, ∠ONL and ∠MNL: ON and MN are on a straight line (MO is a straight line), so they are adjacent (linear pair).
• ∠MNL and ∠PQS: Do they share a side or vertex? No, so this is incorrect. Wait, maybe the original problem's checked options have some errors, but based on adjacent angle definition:
• ∠RQS and ∠PQN (if that's the pair) share Q and a side.
• ∠PQS and ∠PQN share Q and PQ.
• ∠ONL and ∠MNL share N and NL.
• The incorrect one is ∠MNL and ∠PQS as they don't share a side or vertex. But the problem's checked options: Wait, maybe the correct pairs are ∠RQS and ∠PQN, ∠PQS and ∠PQN, ∠ONL and ∠MNL. The pair ∠MNL and ∠PQS is incorrect. But the question is to select all pairs of adjacent angles. So the correct pairs (from the options, assuming labels are correct) are:
• ∠RQS and ∠PQW (if W is N)
• ∠PQS and ∠PQW
• ∠ONL and ∠MNL
• The last pair ∠MNL and ∠PQS is incorrect. But the problem's checked options: Maybe the intended correct pairs are the first three (excluding the last). But based on the problem's given checked boxes, but the correct adjacent angle pairs (using definition) are:

Wait, let's re - express:

Adjacent angles must have:

1. Common vertex.
2. Common side.
3. Non - common sides are distinct rays.

So:

• ∠RQS and ∠PQN: Common vertex Q, common side QS (assuming), so adjacent.
• ∠PQS and ∠PQN: Common vertex Q, common side PQ, so adjacent.
• ∠ONL and ∠MNL: Common vertex N, common side NL, so adjacent.
• ∠MNL and ∠PQS: No common vertex or side, so not adjacent.

So the correct pairs (from the options) are ∠RQS and ∠PQW (or ∠PQN), ∠PQS and ∠PQW (or ∠PQN), ∠ONL and ∠MNL. The pair ∠MNL and ∠PQS is incorrect. But the problem's initial checked options may have an error, but based on the task, we need to identify the correct adjacent angle pairs.

Answer:

The correct pairs of adjacent angles are $\angle RQS$ and $\angle PQN$ (or the labeled pair), $\angle PQS$ and $\angle PQN$, $\angle ONL$ and $\angle MNL$. (Note: Correcting the incorrect pair $\angle MNL$ and $\angle PQS$ which is not adjacent)

But if we go by the problem's options (assuming label typos), the adjacent angle pairs are:

• $\angle RQS$ and $\angle PQW$ (or the intended pair)
• $\angle PQS$ and $\angle PQW$ (or the intended pair)
• $\angle ONL$ and $\angle MNL$