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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.

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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.