Answer
$m\widehat{BTC}=90^{\circ}+128^{\circ}=218^{\circ}$
Work Step by Step
We must know that the measure of a major arc is equal to the measure of the related minor arc subtracted from the angle $360^{\circ}$.
In the given question, we can see that the corresponding angle of major $\widehat{BTC}$ is $\angle BPT+\angle TPC$ .
This implies that
$m\widehat{BTC}=m\angle BPT+m\angle TPC$
or, $m\widehat{BTC}=90^{\circ}+128^{\circ}=218^{\circ}$
