# Chapter 6 - The Circular Functions and Their Graphs - 6.1 Radian Measures - 6.1 Exercises - Page 573: 10

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: $a = \frac{\frac{4}{3}\times 180}{\pi}$ $a = 240$

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