Answer
$308^{\circ}$
Work Step by Step
We must know that the measure of a minor arc is equal to the measure of its corresponding central angle.
In the given question, we can see that the related minor arc of major $\widehat{CBD}$ is $\widehat{CD}$ .
This implies that
$m\widehat{CBD}=360-m\widehat{CD}$.
We have $m\widehat{CD}=m\angle CPD=180^{\circ}-128^{\circ}-52^{\circ}$
Thus, $m \widehat{CBD}=360^{\circ}-52^{\circ}=308^{\circ}$