Multiple choice

The angle subtended by an arc of length $12cm $ at the center of circle whose circumference is $60cm $ is .

  1. 72

  2. 36

  3. 18

  4. None.
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A Correct answer
Explanation

The ratio of the arc length to the total circumference is equal to the ratio of the central angle to 360 degrees. Thus, 12/60 = angle/360. This simplifies to 1/5 = angle/360, so the angle is 360/5 = 72 degrees.

AI explanation

The arc of length 12 centimeters represents a fraction of the total circumference of 60 centimeters, which is 12 divided by 60, or 1 over 5. We multiply this fraction by the total 360 degrees in a circle to find the central angle, giving 360 divided by 5. The result is 72 degrees.

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