An angle is a geometric figure formed by two rays sharing a common endpoint. This common endpoint is called the vertex, and the two rays are called the sides or arms of the angle.

An angle is a geometric figure formed by two rays sharing a common endpoint. This common endpoint is called the vertex, and the two rays are called the sides or arms of the angle.

Let's evaluate the given options:

• "An angle is part of a line that has one endpoint and extends forever in one direction." This describes a ray.
• "An angle is formed where two rays meet at a common endpoint." This is the correct definition of an angle. The common endpoint is the vertex, and the two rays are the sides of the angle.
• "An angle is the point where two rays meet." The point where two rays meet is called the vertex, not the angle itself. The angle is the figure formed by the two rays.
• "An angle extends forever in both directions." This describes a line.

Therefore, the best description of an angle is that it is formed where two rays meet at a common endpoint.

The final answer is $\boxed{\text{An angle is formed where two rays meet at a common endpoint.}}$