If you don't have two rays, can you have an angle?

  Yes

Step-by-step explanation:

You can define an angle of interest at any point of intersection of any real or virtual lines, curves, planes, or surfaces, or combination thereof. We often measure the angle between our present location and two different other locations (horizon, stars, objects of one sort or another). The "rays" involved are virtual (non-existent, imaginary, conceptual) rather than real. We also often measure angles between real physical objects, things other than the idealized set of infinitesimal points that make up a ray.