Identify the relationship between and .

a) Find $\angle$CBD

Step 1: Identify the relationship between $\angle$CAD and $\angle$CBD.
$\angle$CAD and $\angle$CBD are angles subtended by the same arc CD at the circumference.
Angles subtended by the same arc at the circumference are equal.

$$\angle\text{CBD} = \angle\text{CAD}$$ $$\angle\text{CBD} = 30^\circ$$

Reason: Angles in the same segment are equal.
The final answer is $\boxed{\text{30}^\circ}$.

b) Find $\angle$OBD

Step 1: Find $\angle$BOC.
Since A, O, C are collinear and AE is a straight line, $\angle$AOB and $\angle$BOC are supplementary angles.

$$\angle\text{BOC} = 180^\circ - \angle\text{AOB}$$ $$$$