https://file.aiquickdraw.com/mathbot/file/172971109382070t88h5h.jpg

In the given figure, we are asked to determine the vertical angle to ∠UST.

**Definition**: Vertical angles are the angles that are opposite each other when two lines intersect. They are always congruent (equal in measure).

Looking at the diagram, the two intersecting lines are \(\overrightarrow{UT}\) and \(\overrightarrow{RS}\). The angle ∠UST is formed by the intersection of line \(\overrightarrow{UT}\) and the horizontal line passing through \(S\).

The angle vertically opposite to ∠UST is ∠TSR, which is on the opposite side of the intersection point \(S\).

Therefore, the correct answer is:

\[
\boxed{\angle TSR}
\]

Would you like any further details or have additional questions?

Here are some related questions:
1. What are congruent angles?
2. Can vertical angles ever be non-congruent?
3. How do vertical angles relate to parallel lines?
4. What is the sum of two vertical angles?
5. How do you prove that two angles are vertical?

**Tip**: Vertical angles are always congruent regardless of the angle size or the orientation of the lines intersecting.

Which angle is a vertical angle to ∠UST?

Find out how to determine the vertical angle to ∠UST using the vertical angles theorem. This geometry problem involves understanding intersecting lines and opposite angles. Suitable for students in Grades 7-9.

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