#### Answer

The angle is $240$ degrees.

#### Work Step by Step

The area of a sector is
$A = 0.5 \times R^2 \times a$
where R is the radius, and a is the central angle in radians.
lets use the equation:
$96\pi = 0.5 \times 12^2 \times a$
$96 = 72 a$
$a = \frac{4}{3}\pi$
The angle is in radians, so lets convert it to degrees:
$a = \frac{\frac{4}{3}\times 180}{\pi}$
$a = 240$