1. The problem asks to determine which pairs of angles are adjacent among the given pairs: $\angle 5$ and $\angle 10$, $\angle 2$ and $\angle 9$, $\angle 2$ and $\angle 10$, $\angle 11$ and $\angle 12$. 2. **Definition of adjacent angles:** Two angles are adjacent if they share a common vertex and a common side, and their interiors do not overlap. 3. Analyze each pair: - $\angle 5$ and $\angle 10$: These angles are formed by different intersecting lines and do not share a common side. Therefore, they are **not adjacent**. - $\angle 2$ and $\angle 9$: These angles are on different intersections and do not share a common side. Therefore, they are **not adjacent**. - $\angle 2$ and $\angle 10$: These angles are formed at the intersection of the diagonal line with the vertical and horizontal lines. They share a common vertex and a common side (the diagonal line), so they are **adjacent**. - $\angle 11$ and $\angle 12$: These angles are formed by the intersection of the diagonal line with the vertical line. They share a common vertex and a common side, so they are **adjacent**. 4. **Final answer:** Among the given pairs, only $\angle 2$ and $\angle 10$, and $\angle 11$ and $\angle 12$ are adjacent angles.