Applying the theorem that angles subtended by the same arc are equal we have that
a = b = 45 degrees
What is the theorem about
If two angles in a circle subtend equal arcs, they are congruent or equal.
This is a specific instance of the angles subtended by the same arc are equal theorem, which asserts that when two angles subtend the same arc in a circle, those angles are identical in measure.
The subtended arc in this case is arc BC