Question: What is an angle that is adjacent to $\angle 2$?
1. **State the problem:** We need to find an angle adjacent to $\angle 2$ formed by two intersecting lines.
2. **Recall the definition:** Adjacent angles share a common side and a common vertex but do not overlap.
3. **Identify angles around the intersection:** The four angles are $\angle 1$, $\angle 2$, $\angle 3$, and $\angle 4$.
4. **Check adjacency with $\angle 2$:**
- $\angle 1$ is opposite $\angle 3$, not adjacent to $\angle 2$.
- $\angle 3$ shares only a vertex but no common side with $\angle 2$ (they are vertical angles).
- $\angle 4$ shares a common side and vertex with $\angle 2$, so it is adjacent.
5. **Conclusion:** The angle adjacent to $\angle 2$ is $\angle 4$.
**Final answer:** $\boxed{4}$