Compute $\dfrac{25\pi}{60\pi}$ and simplify the result. What fraction of the circle is this?

The central angle corresponding to an arc takes up the same fraction of $360^\circ$ as the arc length takes of the full circumference. Use your fraction from the previous hint to find the angle.

In Desmos, type 25*pi/(60*pi) and observe the simplified value; this is the fraction of the circle represented by arc $AB$.

Multiply that fraction by 360 in Desmos (for example, type (25*pi/(60*pi))*360 as one expression); the resulting value is the measure in degrees of $\angle AOB$.

In a circle, the ratio of an arc’s length to the entire circumference equals the ratio of its central angle (in degrees) to $360$.

So for arc $AB$ and angle $\angle AOB$:

You are told the arc length of minor arc $AB$ is $25\pi$ and the circumference is $60\pi$.

So the fraction of the circle that arc $AB$ represents is

The $\pi$ terms cancel, so this simplifies to

Since $m\angle AOB$ must be the same fraction of $360^\circ$ as the arc is of the circumference, we have

Multiply both sides by $360$:

Therefore, the measure of $\angle AOB$ is $150^\circ$, which corresponds to choice B.