To solve the problem we must know the concept of the Center angle theorem. The measure of the center angle ∠AOC is 160°.
What is the central angle theorem?
According to the central angle theorem, if an arc of a circle makes an angle with any point on the circumference of that circle then the measure of that angle is half the angle made by that arc at the center of the circle.
Given to us
∠ABC = 80°
As we already know the angle made by Arc AC at point B, therefore, the center angle made by ARC AC at the center will be twice of it. Therefore,
∠AOC = 2∠ABC
∠AOC = 2(80°)
∠AOC = 160°
Hence, the measure of the center angle ∠AOC is 160°.
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