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What is the measure of the central angle of a circle with radius 18 centimeters that intercepts a 12pi centimeters arc?

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Answer:

Explanation:

We'll use s = rt where s is arc length, r is the radius, and t is the angle in radians. After we find the angle in radians, we'll convert it to degrees to get the central angle.


12\pi=18t so


t=(2\pi)/(3)

That's the arc length in radians. Radians does not measure the central angle so we convert using the fact that pi is the same as 180 degrees:


(2\pi)/(3)*(180)/(\pi)

The pi's cancel out and 3 goes into 180 60 times, and 60 times 2 is 120, so the angle measure in degrees is 120

User Aditya Hajare
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