1. **State the problem:** Identify which angles are vertical to angle $\angle 6$. 2. **Recall the definition:** Vertical angles are pairs of opposite angles made by two intersecting lines. They are always equal. 3. **Analyze the diagram:** Given six rays intersecting at a point, $\angle 6$ is on the right side. 4. **Find the vertical angle:** The angle directly opposite $\angle 6$ across the vertex is $\angle 3$. 5. **Conclusion:** The angle vertical to $\angle 6$ is $\angle 3$. **Final answer:** $\angle 3$ is vertical to $\angle 6$.