1. **State the problem:** We need to find which angles are supplementary to angle $\angle 2$. Supplementary angles are two angles whose measures add up to $180^\circ$. 2. **Recall the rule:** If two angles form a linear pair (they are adjacent and their non-common sides form a straight line), then they are supplementary. 3. **Analyze the diagram and angles:** - $\angle 2$ is between the bottom-left diagonal ray and the upward vertical ray. - $\angle 4$ is between the upper-right diagonal ray and the rightward ray. - $\angle 5$ is between the rightward ray and the downward vertical ray. - $\angle 1$ is between the downward vertical ray and the bottom-left diagonal ray. - $\angle 3$ is between the upward vertical ray and the upper-right diagonal ray. 4. **Check which angles form a linear pair with $\angle 2$:** - $\angle 1$ shares the bottom-left diagonal ray with $\angle 2$ and together with $\angle 2$ they form a straight line along the bottom-left diagonal and downward vertical rays. - $\angle 3$ shares the upward vertical ray with $\angle 2$ and together they form a straight line along the upward vertical and upper-right diagonal rays. 5. **Conclusion:** $\angle 1$ and $\angle 3$ are supplementary to $\angle 2$ because they form linear pairs with it. **Final answer:** $\angle 1$ and $\angle 3$ are supplementary to $\angle 2$.