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A circle has a circumference of 6\blue{6}. It has an arc of length 11. What is the central angle of the arc, in degrees? ∘^\circ A circle with a circumference of six units. The central angle is highlighted along with the corresponding arc. The arc is one unit long.

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Full solution

Q. A circle has a circumference of 6\blue{6}. It has an arc of length 11. What is the central angle of the arc, in degrees? ∘^\circ A circle with a circumference of six units. The central angle is highlighted along with the corresponding arc. The arc is one unit long.
  1. Find Fraction of Circumference: Find the fraction of the circumference that the arc length represents. Fraction of circumference = arc lengthcircumference=16 \frac{\text{arc length}}{\text{circumference}} = \frac{1}{6}
  2. Convert to Degrees: Convert the fraction to degrees. Since a full circle is 360360 degrees, multiply the fraction by 360360. Central angle = (16)×360=60\left( \frac{1}{6} \right) \times 360 = 60 degrees

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