Yeah I got 110 degrees for angle A but it seems like not enough information is given to find angles B and C.

If you take that radius and extend it to the other end of the circle, and assume that vertex A is where it meets the circle, like this:



Well then B+D = 90 degrees because it's an inscribed angle that cuts out 180 degrees of the circle, and D = 50 degrees because it cuts out 100 degrees of the circle, and C = 30 degrees because it cuts out the same arc as the other 30 degree angle. So B = 40 degrees and A = 110 degrees.

However there's no reason why A needs to be in that same place, but when you move the location of A around the circle doesn't change the measure of A, but it does change B and C. Given no information about where A is I don't see how you can determine the measures of B and C.