Answer
$m \widehat{BCD}=270^{\circ}$
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 $\widehat{BCD}$ is $\widehat{BD}$ .
This implies that
$m\widehat{BCD}=360-m\widehat{BD}$.
We have $m\widehat{BD}=m\angle BPD=90^{\circ}$
Thus, $m \widehat{BCD}=360^{\circ}-90^{\circ}=270^{\circ}$
