Answer
$\displaystyle \theta= \frac{s}{r}\cdot\frac{180^{\mathrm{o}}}{\pi}$
Work Step by Step
Converting between Degrees and Radians
1. Multiply a degree measure by $\displaystyle \frac{\pi}{180}$ radian and simplify to convert to radians.
2. Multiply a radian measure by $\displaystyle \frac{180^{\mathrm{o}}}{\pi}$ and simplify to convert to degrees.
Arc length s (for central angle $\theta$):$ \quad s=r\theta$, where $\theta$ is in radians
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$ s=r\theta$, solving for $\theta$
$\displaystyle \theta=\frac{s}{r}$
Since $\theta$ is in radians, (see converting, case 2)
$\displaystyle \theta= \frac{s}{r}\cdot\frac{180^{\mathrm{o}}}{\pi}$
