Let the radius of the sector be r, the radius of the circle be r, and the central angle of the sector be n.

Because the sector area is equal to the circle area.

So n/360 π r 2 = π r 2

(r/R)^2=360 /n

The radius of the sector is equal to twice the radius of the circle.

4=360 /n

n=90

Let the central angle of the sector be α and the radius 2r; The radius of a circle is R.

Available: (a/360) * π * (2r) 2 = π * r 2.

The solution is a=90 degrees.