A Simple Trigonometry question about Cosines

This is a very simple question I am sure for anyone who works with mathematics or is currently studying mathematics. Unfortunately, I have not touched this stuff in decades and I am a bit rusty.

How do I determine what an angle is on an X and Y grid of a line that intersects a circle drawn on that grid (both the line and the circle are centered at (0,0) )? If we know that point at which the line intersects the circle, how can that be converted into a degreed angle?

Here is another way of asking the same question. If I have an X and Y point on a grid that represents the intersection of two formulas: A straight line (aX = Y) where "a" represents a constant number with a circle( x squared + y squared = radius squared), how would I convert that point into a degree of an angle? The angle would represent the line function albeit only go one direction on the grid. It would be some degree.

If I were to guess, this might be very simple and have something to do with cosine rules.