Let $ABC$ be a triangle with $m(\widehat{A}) = 70^\circ$ and the incenter $I$. If $|BC| = |AC| + |AI|$, then what is the value of $m(\widehat{B})$ in degrees? If the answer is $x^\circ$, what is the value of $x$?

Let's think step by step and output the final answer within \boxed{}.
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