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Definition: Angles are formed by two rays that begin at the same point or share the same endpoint. The angle measures the amount of turn between the two arms and is usually measured in degrees or radians. Where the two rays intersect (come together to meet) is called the vertex. The two rays are sometimes referred to as the arms.
An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle. Under this definition, two angles are congruent provided either can be made to coincide (the vertex and the sides) with the other by a rigid motion.