1. **Problem Statement:** Identify which angle is complementary to \(\angle 2\) given the angles formed by two intersecting lines. 2. **Recall definitions:** - Complementary angles sum to \(90^\circ\). - Supplementary angles sum to \(180^\circ\). - Vertical angles are opposite angles formed by two intersecting lines and are congruent. - Adjacent angles share a common side and vertex. - Congruent angles have equal measure. 3. **Analyze the figure:** - Two lines intersect forming four angles labeled \(\angle 1, \angle 2, \angle 3, \angle 4\). - \(\angle 2\) is adjacent to \(\angle 1\) and \(\angle 4\). - \(\angle 2\) and \(\angle 3\) are vertical angles. 4. **Check complementary pairs:** - Since the lines intersect, adjacent angles like \(\angle 2\) and \(\angle 1\) or \(\angle 2\) and \(\angle 4\) are supplementary (sum to \(180^\circ\)), not complementary. - Vertical angles \(\angle 2\) and \(\angle 3\) are congruent, so their sum is \(2 \times \angle 2\), which cannot be \(90^\circ\) unless \(\angle 2 = 45^\circ\). 5. **Conclusion:** - The only angle that can be complementary to \(\angle 2\) is \(\angle 3\) if \(\angle 2 = 45^\circ\), because vertical angles are equal and their sum would be \(90^\circ\). **Final answer:** \(\boxed{\angle 3}\) is complementary to \(\angle 2\).