I think I see what you're saying. By using

, then then

. This gives me

, giving an output of .42 rads, which converted to degrees comes out to

. This seems like it checks out!

Interestingly enough, I got a somewhat similar figure by dividing the angle of circle A by the ratio of the two circumferences (it ended up looking like 60/ 2.49 rev of A to every 1 rev of B); it's not as accurate compared to the calculations above, but I wasn't sure whether or not to write it off as circumstantial before I got a response on this thread.