Answer
$$m\widehat{TDC}=232^{\circ}$$
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 $\widehat{TDC}$ is $\widehat{TC}$ .
This implies that $m\widehat{TDC}=360^{\circ}-m\widehat{TC}$
We have $m\widehat{TC}=m\angle TPC=128^{\circ}$. This implies that $m\widehat{TDC}=360^{\circ}-128^{\circ}$
or, $m\widehat{TDC}=232^{\circ}$
