Inscribed angles subtended by the same arc are equal.
Central angle is twice any inscribed angle subtended by the same arc.
Angles BDC and BAC are iscribed angles
Angle BOC is a central angle
The three angles are subtended by arc CB.
Measure of angle BDC is equal to measure of angle BAC:

Measure of angle BOC is twice measure of angle BDC:

Then, the measure of angle BCA is 29º and the measure of angle BOC is 58º