Answer
$\theta=1$ radian
Work Step by Step
Step 1: The formula to be used here will be $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of a sector of a circle of radius $r$ and central angle $\theta$.
Step 2: Substituting the values provided by the question into the formula, $8=\frac{1}{2}(4)^{2}\theta$
Step 3: $8=\frac{1}{2}\times(16)\times\theta$
Step 4: $8=8\times\theta$
Step 5: Multiplying both sides by $\frac{1}{8}$,
$8\times\frac{1}{8}=8\times\frac{1}{8}\times\theta$
Step 6: $\theta=1$ radian