Answer
$49.06^{\circ}$
Work Step by Step
The formula to be used here is $s=r\theta$ where $s$ is the arc length, $r$ is the radius and $\theta$ is the angle in radians.
Next, we rearrange the formula to $\theta=\frac{s}{r}$ because $s$ and $r$ are known and $\theta$ is the unknown.
Substituting the values of $r=8.973$ cm and $s=7.683$ cm into the formula and solving using a calculator:
$\theta=\frac{s}{r}=\frac{7.683}{8.973}\approx0.8562$ radian
Converting radians to degrees:
$0.8562$ radian=$0.8562(\frac{180}{\pi})=49.06^{\circ}$