Circle Geometry 3.

From the diagram, the angle $\angle BDC$ is given as $30^\circ$.

Angles subtended by the same arc at the circumference are equal. Both $\angle BAC$ and $\angle BDC$ subtend the arc BC.
Therefore, $\angle BAC = \angle BDC$.

The angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the remaining part of the circle. The central angle $\angle BOC$ subtends arc BC, and the circumference angle $\angle BAC$ also subtends arc BC.

Final values for :
$\angle BDC = \boxed{30^\circ}$
$\angle BAC = \boxed{30^\circ}$
$\angle BOC = \boxed{60^\circ}$