A circle is a curve sketched out by a point moving in a plane. The correct option is B.
What is a circle?
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
In the diagram below, AB and BC are tangent to O. Therefore, the measure of the line segment AB and AC will be equal. And since both are tangent to the circle, therefore, the measure of ∠OAB and ∠OCB will 90°.
Also, given that the measure of arc AC is 120°. Therefore, the measure of angle ∠AOC is 120°. Since the sum of all the angles of a quadrilateral is 360°. Therefore, for quadrilateral ABCO we can write the sum of the angles as,
∠ABC + ∠AOC + ∠OAB + ∠OCB = 360°
∠ABC + 120° + 90° + 90° = 360°
∠ABC = 60°
Now, we simplify each of the given options, therefore, we can write,
A. 240° + 120° = 360°.
Thus, this is not the correct option.
B. (1/2)(240° - 120°) = 60°.
Thus, this is the correct option.
C. (1/2)(240° + 120°) = 180°.
Thus, this is not the correct option.
D. 240° - 120° = 120°.
Thus, this is not the correct option.
Hence, the measure of the ∠ABC is 60°.
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