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An angle is a plane figure formed by two rays that have the same starting point. This common point is called the vertex of the angle and the rays are the sides of the angle.
Angle ABC is formed by two rays, BC and BA, which are referred to as the sides of the angle. The starting points of both rays are identical, originating from point B, which serves as the vertex of the angle.

There are different ways to denote an angle and all involve the symbol in front of the name. One way is to name an angle by its vertex alone. Alternatively, it can be named by using all three points that make up the angle. In this case, the vertex is always in the middle of the name. Additionally, angles within a diagram can be denoted with numbers or lowercase Greek letters.

Using the Vertex Using the Vertex and One Point on Each Ray Using a Number Using Greek Letters
or or or

The measure of an angle, denoted by is the number of degrees between the rays. It is found by applying the Protractor Postulate. When two angles have the same measure, they are said to be congruent.

Interior and Exterior of an Angle

An angle divides the plane into two parts.

  • The region between the sides, or interior of the angle
  • The region outside the sides, or exterior of the angle
These regions can be examined in the following graph.
Interior and Exterior of an angle
Notice that the interior of the angle is the region for which the angle measure is less than