Question

which angles are vertical angles?
∠utv and ∠rqt ∠utv and ∠stq
∠utv and ∠pqo ∠utv and ∠rqo

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. They are opposite each other.

Step2: Analyze each option

• For $\angle UTV$ and $\angle RQT$: These angles are not formed by the intersection of the same two lines in the required non - adjacent, opposite - each - other way.
• For $\angle UTV$ and $\angle STQ$: These are adjacent angles (they share a common side and vertex), so they are not vertical angles.
• For $\angle UTV$ and $\angle PQO$: These angles are not formed by the intersection of the same two lines in the required non - adjacent, opposite - each - other way.
• For $\angle UTV$ and $\angle RQO$: The lines $PR$ and $SV$ intersect at a point (indirectly through the figure's line - intersection structure). $\angle UTV$ and $\angle RQO$ are non - adjacent and opposite each other, which satisfies the definition of vertical angles.

Answer:

$\angle UTV$ and $\angle RQO$