Answer
The angle is $\frac{5\pi}{4}$ in radians and $225^\circ$ in degrees.
Work Step by Step
To find out the angle, we need to employ the formula:
$$s = r\theta$$
which means $$\theta=\frac{s}{r}$$
$s$: the length of the arc
$r$: radius of the circle
$\theta$: the central angle of the arc (in radians)
Here $r = 8$ and $s=10\pi$
So the angle would be (in radians):
$$\theta=\frac{10\pi}{8}=\frac{5\pi}{4}$$
In degrees, that angle would be:
$$\theta=\frac{5\pi}{4}\times\frac{180^\circ}{\pi}=\frac{5\times180^\circ}{4}=225^\circ$$
