You can either use $s = r\theta$ with $\theta$ in radians, or use a proportion with the full circumference: $\dfrac{\text{arc length}}{\text{circumference}} = \dfrac{\text{central angle}}{360}$.

The radius is 10, so the circumference is $2\pi(10)$. Plug $8\pi$ and $10$ into your chosen formula or proportion, then solve step by step for the angle. If you used radians, remember to convert to degrees at the end.

In Desmos, type the expression (8*pi/10)*(180/pi). The value that Desmos returns is the measure of the central angle in degrees.

For a circle, the relationship between arc length $s$, radius $r$, and central angle $\theta$ (in radians) is

Here, $s = 8\pi$ centimeters and $r = 10$ centimeters. We first solve for $\theta$ in radians.

Use $s = r\theta$ and plug in the given values:

Divide both sides by 10:

So the central angle is $\tfrac{4\pi}{5}$ radians. Now convert this to degrees.

To convert radians to degrees, multiply by $\dfrac{180}{\pi}$:

The $\pi$ cancels, and you get

So the measure of the central angle is $144$ degrees, which corresponds to choice B.