Answer
$m\widehat {BC}=135^{\circ}$
Work Step by Step
If the $m\widehat {ACB}=270^{\circ}$, and point $C$ bisects arc $ACB$, then $m\widehat {BC}$ is half the $m\widehat {ACB}$ or $m\widehat {BC}=135^{\circ}$.
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