Can we do this without guess and check?
I guess that depends, since we aren't given the radius...
-Dan
Edit: I guess the radius was mentioned. (Ahem!)
The perimeter $P$ of the given sector is:
$ \displaystyle P=2n+n\frac{360}{n}\cdot\frac{\pi}{180}=2(n+\pi)$
So, we want:
$ \displaystyle 20<P<30$
$ \displaystyle 20<2(n+\pi)<30$
$ \displaystyle 10<n+\pi<15$
Can you continue