Question

select all the pairs of vertical angles.
∠rsp and ∠tsu
∠rsp and ∠tsp
∠opn and ∠ops
∠qpn and ∠ops

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. They are opposite each other and are equal in measure.

Step2: Analyze each pair

• For $\angle RSP$ and $\angle TSU$: Lines $RT$ and $UN$ intersect at point $S$. $\angle RSP$ and $\angle TSU$ are opposite each other at the intersection of these two lines, so they are vertical angles.
• For $\angle RSP$ and $\angle TSP$: These two angles share a common side ($\overrightarrow{SP}$) and do not meet the criteria of vertical - angles.
• For $\angle OPN$ and $\angle OPS$: These two angles share a common side ($\overrightarrow{OP}$) and are not vertical angles.
• For $\angle QPN$ and $\angle OPS$: Lines $OQ$ and $UN$ intersect at point $P$. $\angle QPN$ and $\angle OPS$ are opposite each other at the intersection of these two lines, so they are vertical angles.

Answer:

$\angle RSP$ and $\angle TSU$, $\angle QPN$ and $\angle OPS$