# Geometry

## Angles

An angle in geometry is the union of two rays with a common endpoint. The common endpoint is called the "vertex" and the rays are called the "sides." Angle ABC is the union of BA and BC. When there is no danger of confusion, an angle can be named by its vertex alone. It is also handy from time to time to name an angle with a letter or number written in the interior of the angle near the vertex. Thus angles ABC, B, and x are all the same angle.

Figure 1. Illustration by Hans & Cassidy. Courtesy of Gale Group.

When the two sides of an angle form a line, the angle is called a "straight angle." Straight angles have a measure of 180°. Angles which are not straight angles have a measure between 180° and 0°. The "reflex" angles, whose measures exceed 180°, encountered in other branches of mathematics are not ordinarily used in geometry. If the sum of the measures of two angles is 180°, the angles are said to be "supplementary." "Right" angles have a measure of 90°. Lines which form right angles are also said to be perpendicular. If the sum of the measures of two angles is 90°, the angles are called "complementary." Angles which are smaller than a right angle are called "acute." Those which are bigger than a right angle but smaller than a straight angle are called "obtuse." When two lines intersect, they form two pairs of "opposite" or "vertical" angles. Vertical angles are equal.

A ray which divides an angle into two equal angles is called an angle "bisector." Points on an angle bisector are equidistant from the sides of the angle.