Question

which angles are alternate interior angles? ∠stw and ∠vwt ∠stw and ∠vwy ∠stw and ∠xwt ∠stw and ∠utr

Explanation:

Step1: Recall alternate - interior angles definition

Alternate - interior angles are two non - adjacent angles that lie between two lines and on opposite sides of a transversal.

Step2: Analyze each option

For $\angle STW$ and $\angle VWT$, they lie between lines $SV$ and $XU$ and on opposite sides of transversal $YR$. They are alternate - interior angles.
For $\angle STW$ and $\angle VWY$, $\angle VWY$ is not an interior angle between the two lines formed by $SV$ and $XU$ with respect to transversal $YR$.
For $\angle STW$ and $\angle XWT$, $\angle XWT$ is not in the correct position to be an alternate - interior angle with $\angle STW$.
For $\angle STW$ and $\angle UTR$, $\angle UTR$ is not an interior angle between the two lines formed by $SV$ and $XU$ with respect to transversal $YR$.

Answer:

$\angle STW$ and $\angle VWT$