this is because a bisector is always a cross or any other shape that cuts something into its exact half (unlike intersect which can cut any shape in any form unlike its exact half )
so, as you can see in the figure, angle BOC is bisecting* AOC at its exact half, angle BOC is the answer.
The definition of an angle bisector is that it divides an angle into two congruent angles. ∠AOC is divided by angle bisector OB into angles ∠AOB and ∠BOC, hence those two angles are congruent.
