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

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 \(x\)?

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

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