Answer
The central angle is $32.2^{\circ}$
Work Step by Step
Let $\theta$ be the angle in radians. Let $r$ be the radius. We can use the arc length $d$ to make an expression for the radius $r$:
$d = \theta ~r$
$r = \frac{d}{\theta}$
Let $A$ be the area of the sector. Then the ratio of the angle $\theta$ to $2\pi$ is equal to the ratio of the sector area to the area of the whole circle.
$\frac{\theta}{2\pi} = \frac{A}{\pi ~r^2}$
$\frac{\theta}{2\pi} = \frac{A}{\pi ~(\frac{d}{\theta})^2}$
$\frac{\theta}{2\pi} = \frac{A~\theta^2}{\pi ~d^2}$
$\theta = \frac{d^2}{2~A}$
$\theta = \frac{(6.0~cm)^2}{(2)(16~cm^2)}$
$\theta = 1.125~rad$
We can convert the angle $\theta$ to degrees:
$\theta = (1.125~rad)(\frac{180^{\circ}}{2\pi~rad}) = 32.2^{\circ}$
The central angle is $32.2^{\circ}$
