Given:
The area of a sector, A=74.84 sq. in.
The radius of the sector, r=8 in.
Now, the expression for the area of a sector can be written as,
[tex]A=\frac{\theta}{360^{\circ}}\times\pi r^2[/tex]
Here, θ is the central angle in degrees.
Rearrange the above equation and substitute values to find the angle θ.
[tex]\begin{gathered} \theta=\frac{A}{\pi r^2}\times360^{\circ} \\ =141^{\circ} \end{gathered}[/tex]
