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Definition: An angle (in full, plane angle) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other.
Example: A straight line with a vertex in the middle can be considered an angle of 180 degrees. A straight line with a vertex on an end can be considered an angle of 0 or 360 degrees.