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Geometry: Constructions

Angle Pairs



Complementary and Supplementary Angles

Special names are given to pairs of angles whose sums equal either 90 or 180 degrees. A pair of angles whose sum is 90 degrees are called complementary angles. Each angle is the other angle's complement. Likewise, if two angles sum to 180 degrees, they are called supplementary angles.

It is important to remember that these terms are only relative. An angle is only supplementary or complementary to another specific angle. A single angle, when considered alone, can be neither supplementary nor complementary--it can only take on one of these properties when considered as one of a pair of angles. Take a look at the examples below.

Figure %: Angles ABC and CBD are complementary, whereas angles KHJ and JHI are supplementary.

Vertical Angles

When two lines (or segments) intersect, special names are given to each pair of angles that lie opposite each other. These angles, which are formed by rays that point in opposite directions, are called vertical angles. Vertical angles are always congruent.

Figure %: Two pairs of vertical angles.
Angles DAC and BAE are vertical angles. Angles DAB and CAE are also vertical angles.