What is the name of the point where the rays of an angle meet?

The point where the rays of an angle meet is known as the vertex of an angle. This point is crucial in defining the angle itself; the two rays that originate from the vertex extend outward to form the angle. In geometry, understanding the vertex helps in identifying and working with angles, including their measurements and properties.

While other terms might be related to geometric concepts, they do not specifically define the point where the rays of an angle converge. The focus point pertains more to optics and the behavior of light, endpoints refer to points at the ends of line segments, and intersection typically describes the point where two lines or paths cross but does not specifically apply to angles. Therefore, the correct terminology for the point where angle rays meet is indeed the vertex of the angle.