1. The problem asks which angles are supplementary to \(\angle 6\). Supplementary angles are two angles whose measures add up to \(180^\circ\).\n\n2. Given two intersecting lines, adjacent angles formed by these lines are supplementary because they form a straight line (linear pair).\n\n3. \(\angle 6\) is adjacent to \(\angle 5\) and \(\angle 1\) because they share a common side and their non-common sides form a straight line. Therefore, \(\angle 6 + \angle 5 = 180^\circ\) and \(\angle 6 + \angle 1 = 180^\circ\).\n\n4. \(\angle 3\) and \(\angle 2\) are not adjacent to \(\angle 6\) and do not form a linear pair with it, so they are not supplementary to \(\angle 6\).\n\n5. Hence, the supplementary angles to \(\angle 6\) are \(\angle 5\) and \(\angle 1\).