Yes, it is correct that if ray OC is the bisector of ∠AOB, then m∠AOC = m∠COB.
This is because the definition of a bisector is a line, ray, or line segment that divides an angle into two equal parts. In this case, ray OC is dividing ∠AOB into two equal angles, ∠AOC and ∠COB.
Therefore, by definition, m∠AOC = m∠COB.
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