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.