A semicircle has half the circumference of the full circle.

The two labeled arcs on the semicircle add to the semicircle’s total arc length.

In Desmos, type 160*pi/2 to get the length of the semicircle arc from $A$ to $C$.

Type the result from step 1 divided by 4 to get the value of $x$ (since $3x+x$ makes the semicircle).

Multiply the value of $x$ by 3. That result corresponds to the arc labeled $3x$, which is minor arc $\overset{\frown}{AB}$ in the figure.

Because $\overline{AC}$ is a diameter in the figure, the arc from $A$ to $C$ along the top is a semicircle.

So the length of arc $\overset{\frown}{AC}$ (top semicircle) is half the circumference:

On that top semicircle, the arc from $A$ to $B$ is labeled $3x$, and the arc from $B$ to $C$ is labeled $x$.

So their total is the semicircle:

Arc $\overset{\frown}{AB}$ is labeled $3x$, so

Therefore, the correct answer is $60\pi$.