complementary and supplementary angles

Some pairs of angles are partners that together fill up a familiar whole — a right angle or a straight line. Naming these partnerships gives two of the most useful relationships in beginning geometry: complementary and supplementary angles.

Two angles are complementary if their measures add to 90°; each is called the complement of the other. Two angles are supplementary if their measures add to 180°; each is the supplement of the other. So the complement of a 35° angle is 55° (since 35 + 55 = 90), and the supplement of a 35° angle is 145° (since 35 + 145 = 180). The angles need not be next to each other — only their measures matter — but when two angles do sit side by side and together form a right angle or a straight line, they are automatically complementary or supplementary respectively. Two adjacent angles whose non-shared sides form a straight line are called a linear pair, and a linear pair is always supplementary.

These relationships turn geometry problems into quick algebra. If one of two complementary angles is x, the other is 90 - x; if one of two supplementary angles is x, the other is 180 - x. They power countless proofs: because angles forming a straight line are supplementary, and two angles supplementary to the same angle are equal, you can deduce facts like the equality of vertical angles. A simple memory aid: Complementary 'C' comes before Supplementary 'S', and 90 comes before 180.