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Concept

Angle

An angle is the set of points in the plane formed by two different rays that share the same starting point. This common point is called the vertex of the angle and the rays are the sides of the angle.
Two Rays with the same starting point

There are different ways to denote an angle and all involve the symbol in front of the name. For the second notation, the vertex always must be in the middle.

Using the Vertex Using the Vertex and One Point on Each Ray Using a Number
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.

Extra

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 an angle is the region for which the angle measure is less than

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