$$\text{Note: Figure not drawn to scale.}$$

Segments $\overline{OA}$ and $\overline{OB}$ are radii of the semicircle above. Arc $\overgroup{AB}$ has length $2\pi$ and $OA=6$. What is the value of $x$?

Summary Submit Skip Question

We can set a proportion which relates the sector to the entire circle:

$$\frac{\text{arc length}}{\text{circumference}}=\frac{x\degree}{360\degree}$$ $$\frac{2\pi}{2\pi r} = \frac{x\degree}{360 \degree}$$ $$\frac{1}{6}=\frac{x\degree}{360 \degree}$$ $$360=6\cdot x$$ $$x = \boxed{60\degree}$$