A circle has a radius of 8 centimeters. An arc of the circle has a length of 4 centimeters. What is the measure, in degrees, of the central angle that intercepts this arc?

SAT Circles Practice Question 7 (Medium)

Math · Geometry and TrigonometryMedium

A circle has a radius of $8$ centimeters. An arc of the circle has a length of $4\pi$ centimeters. What is the measure, in degrees, of the central angle that intercepts this arc?

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Answer: 90

The circumference is $2\pi(8) = 16\pi$ centimeters. The arc is $\frac{4\pi}{16\pi} = \frac{1}{4}$ of the circle, so the central angle is $\frac{1}{4} \times 360^\circ = 90^\circ$ .

Answering $\frac{\pi}{2}$ gives the angle in radians, but the question asks for degrees.

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