Question

select all the pairs of vertical angles. ∠nor and ∠pom ∠sro and ∠qrt ∠sro and ∠qro ∠nom and ∠srt

Explanation:

Step1: Recall Vertical Angles Definition

Vertical angles are formed by two intersecting lines and are opposite each other, having equal measure.

Step2: Analyze Each Pair

• $\angle NOR$ and $\angle POM$: Lines $NOP$ and $TOM$ intersect at $O$. $\angle NOR$ and $\angle POM$ are opposite (vertical) angles. Correct.
• $\angle SRO$ and $\angle QRT$: Lines $QRS$ and $TRM$ intersect at $R$. $\angle SRO$ (at $R$, between $SR$ and $RO$) and $\angle QRT$ (at $R$, between $QR$ and $RT$) are opposite (vertical) angles. Correct.
• $\angle SRO$ and $\angle QRO$: These are adjacent angles on a straight line (supplementary), not vertical. Incorrect.
• $\angle NOM$ and $\angle SRT$: $\angle NOM$ is at $O$, $\angle SRT$ at $R$; not formed by same intersecting lines. Incorrect. Wait, re - check: Wait, original options might have errors? Wait, no, let's re - evaluate the correct vertical angle pairs. Wait, the correct vertical angle pairs should be:
• At point $R$: When lines $QRS$ and $TRM$ intersect, vertical angles are $\angle SRO$ and $\angle QRT$ (since $\angle SRO$: sides $SR$ and $RO$; $\angle QRT$: sides $QR$ and $RT$ ( $RT$ is opposite to $RO$? Wait, maybe better to look at intersection points.
• At point $O$: Lines $NOP$ and $TOM$ intersect, so vertical angles are $\angle NOR$ and $\angle POM$ (sides $NO$ and $RO$; $PO$ and $MO$) and also $\angle NOM$ and $\angle POR$ (but not in options). Wait, the given options: The correct vertical angle pairs among the options are $\angle NOR$ and $\angle POM$ (intersection at $O$: opposite angles) and $\angle SRO$ and $\angle QRT$ (intersection at $R$: opposite angles). The other options: $\angle SRO$ and $\angle QRO$ are adjacent (linear pair), $\angle NOM$ and $\angle SRT$ are not vertical. So the correct pairs are $\angle NOR$ and $\angle POM$, $\angle SRO$ and $\angle QRT$.

Answer:

The correct pairs of vertical angles are $\boldsymbol{\angle NOR}$ and $\boldsymbol{\angle POM}$, $\boldsymbol{\angle SRO}$ and $\boldsymbol{\angle QRT}$. (If we consider the checkmarks in the original, but the incorrect ones should be un - checked. But based on vertical angle definition, the correct pairs are $\angle NOR$ and $\angle POM$, $\angle SRO$ and $\angle QRT$)