QuestionDecember 13, 2025

What is the measure of the central angle of a circle with radius 30 centimeters that intercepts an 18pi centimeters arc? Enter your answer in the box. square ^circ

What is the measure of the central angle of a circle with radius 30 centimeters that intercepts an 18pi centimeters arc? Enter your answer in the box. square ^circ
What is the measure of the central angle of a circle with radius 30 centimeters that intercepts an 18pi centimeters arc? Enter your answer in the box. square ^circ

Solution
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Answer

108^\circ Explanation 1. Use arc length formula Arc length s = r\theta, where \theta is in radians. 2. Solve for \theta 18\pi = 30 \cdot \theta \implies \theta = \frac{18\pi}{30} = \frac{3\pi}{5} radians. 3. Convert radians to degrees 1 radian = \frac{180^\circ}{\pi}, so \theta = \frac{3\pi}{5} \times \frac{180^\circ}{\pi} = \frac{3 \times 180^\circ}{5} = 108^\circ.

Explanation

1. Use arc length formula<br /> Arc length $s = r\theta$, where $\theta$ is in radians.<br />2. Solve for $\theta$<br /> $18\pi = 30 \cdot \theta \implies \theta = \frac{18\pi}{30} = \frac{3\pi}{5}$ radians.<br />3. Convert radians to degrees<br /> $1$ radian $= \frac{180^\circ}{\pi}$, so $\theta = \frac{3\pi}{5} \times \frac{180^\circ}{\pi} = \frac{3 \times 180^\circ}{5} = 108^\circ$.
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