#### Answer

90 $in^{2}$

#### Work Step by Step

Given area of the circle = 360 $in^{2}$
central angle measures =90$^{\circ}$
In a circle of radius length r , the Area A of the sector whose arc has degree measure m is
A = $\frac{m}{360}$ * $\pi r^{2}$
=
The area of the circle = $\pi r^{2}$ = 360
m= 90
A = $\frac{90}{360}$ * 360
= 90 $in^{2}$