What are the unknown angles in each circle, given the tangent-chord relationship and angle at the circumference?

The angle between the tangent ABT and the chord BC is $\angle CBT = 35^\circ$. By the tangent-chord theorem, this angle is equal to the angle in the alternate segment, which is $\angle BAC$.

The angle at the center $\angle BOC$ subtended by the arc BC is twice the angle at the circumference $\angle BAC$ subtended