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76 degrees.

Step-by-step explanation:

Let as consider O is the center of the circle . So from the figure it is clear that

By central angle theorem, central angle subtended by an arc is twice of inscribed angle of the same arc.

We know that, and angle BOD is the central angle subtended by arc BD.

Now,

Therefore, the measure of arc BC is 76 degrees.

here is the

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