High School

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Circle C is shown. Line segments AC and BC are radii. The length of CB is 18. Angle ACB is 140 degrees. Arc AB is labeled as s.

What is the measure of the central angle?

Answer :

The measure of the central angle in the circle described is 140 degrees because it is given that angle ACB, which is the central angle, measures 140 degrees.

In this geometry problem involving circles, the central angle can be determined directly from the given information. The student provides the radius BC which is 18 units long, and the central angle ACB which measures 140 degrees.

The central angle is defined as the angle subtended at the centre of the circle by an arc on the circumference. Therefore, the measure of the central angle in question is 140 degrees. This is because the line segments AC and BC are radii of circle C, and angle ACB is given directly as 140 degrees, making it the central angle to arc AB, also denoted as s.

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