1. **State the problem:** We need to find which angles are supplementary to \(\angle 2\). Supplementary angles are two angles whose measures add up to \(180^\circ\).\n\n2. **Recall the rule:** When two lines intersect, opposite (vertical) angles are equal, and adjacent angles on a straight line are supplementary.\n\n3. **Analyze the diagram:** \(\angle 2\) and \(\angle 4\) are adjacent and form a straight line, so they are supplementary.\n\n4. **Check other angles:** \(\angle 1\) and \(\angle 3\) are vertical angles to \(\angle 4\) and \(\angle 2\) respectively, so they are equal but not supplementary to \(\angle 2\). \(\angle 5\) is not adjacent to \(\angle 2\) and does not form a straight line with it.\n\n**Final answer:** The angle supplementary to \(\angle 2\) is \(\angle 4\).