Question

select all the pairs of adjacent angles.

Explanation:

Step1: Recall the definition of adjacent angles

Adjacent angles share a common vertex and a common side, and have no overlapping interior.

Step2: Analyze each pair

• For $\angle POR$ and $\angle SRT$: They share a common vertex \(O\) (for \(\angle POR\)) and \(R\) (for \(\angle SRT\)) which is incorrect. Wait, no! Wait, actually, looking at the lines. Wait, no, adjacent angles must share a common vertex and a common side. Wait, no, let's re - check.

Wait, no, adjacent angles: two angles are adjacent if they have a common side and a common vertex and no common interior points.

• $\angle NOM$ and $\angle POR$: They have no common side or vertex. Incorrect.
• $\angle SRT$ and $\angle SRO$: They share vertex \(R\) and side \(RS\). Correct.
• $\angle POM$ and $\angle SRO$: They have no common side or vertex. Incorrect.

Wait, no, wait, let's re - check the problem. Wait, the first pair \(\angle POR\) and \(\angle SRT\): no, that's wrong. Wait, maybe there was a mis - identification. Wait, actually, adjacent angles. Let's check each option again:

• Option 1: \(\angle POR\) and \(\angle SRT\)

These two angles do not share a common vertex or a common side. So this is incorrect.

• Option 2: \(\angle NOM\) and \(\angle POR\)

They do not share a common vertex or a common side. Incorrect.

• Option 3: \(\angle SRT\) and \(\angle SRO\)

They share the vertex \(R\) and the side \(RS\). Correct.

• Option 4: \(\angle POM\) and \(\angle SRO\)

They do not share a common vertex or a common side. Incorrect.

Wait, no, wait, maybe the original problem had a different figure interpretation. Wait, adjacent angles:

• Two angles are adjacent if they have a common side and a common vertex and their interiors do not overlap.

Looking at the figure (assuming standard line - intersection):

• For \(\angle SRT\) and \(\angle SRO\): they share vertex \(R\) and side \(RS\). So they are adjacent.

Answer:

\(\angle SRT\) and \(\angle SRO\)