1. **Problem Statement:** Given two parallel lines $\overrightarrow{RT}$ and $\overrightarrow{UW}$, and a transversal line crossing points $Q$, $S$, $V$, and $X$, identify which pairs of angles are vertical angles. 2. **Definition of Vertical Angles:** Vertical angles are pairs of opposite angles made by two intersecting lines. They are always equal. 3. **Analyze the given pairs:** - $\angle UVX$ and $\angle WVS$: These angles share vertex $V$ and are formed by the intersection of lines $UV$ and $WV$. They are opposite each other, so they are vertical angles. - $\angle UVX$ and $\angle TSV$: These angles do not share the same vertex and are not opposite angles formed by intersecting lines. - $\angle UVX$ and $\angle TSQ$: These angles are on different vertices and lines. - $\angle UVX$ and $\angle WWX$: These angles do not share the same vertex and are not opposite angles. 4. **Conclusion:** The vertical angles are $\angle UVX$ and $\angle WVS$. **Final answer:** $\boxed{\angle UVX \text{ and } \angle WVS}$