Question

select all the pairs of alternate interior angles.

Explanation:

Step1: Recall alternate - interior angles definition

Alternate - interior angles are formed when a transversal intersects two lines. They are on the interior of the two lines and on opposite sides of the transversal.

Step2: Analyze each pair

• For $\angle RQT$ and $\angle UTQ$: They are on the interior of the lines formed by $\overrightarrow{UR}$ and $\overrightarrow{SP}$ and on opposite sides of the transversal $\overrightarrow{VO}$, so they are alternate - interior angles.
• For $\angle STQ$ and $\angle RQT$: They are on the interior of the lines formed by $\overrightarrow{UR}$ and $\overrightarrow{SP}$ and on opposite sides of the transversal $\overrightarrow{VO}$, so they are alternate - interior angles.
• For $\angle UTQ$ and $\angle PQT$: They are on the interior of the lines formed by $\overrightarrow{UR}$ and $\overrightarrow{SP}$ and on opposite sides of the transversal $\overrightarrow{VO}$, so they are alternate - interior angles.
• For $\angle UTV$ and $\angle UTQ$: $\angle UTV$ and $\angle UTQ$ are adjacent angles, not alternate - interior angles.

Answer:

$\angle RQT$ and $\angle UTQ$, $\angle STQ$ and $\angle RQT$, $\angle UTQ$ and $\angle PQT$