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1. I guess that depends, since we aren't given the radius...

-Dan

Edit: I guess the radius was mentioned. (Ahem!)

2. 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

N can equal 7,8,9,10, or 11?

4. Originally Posted by Ilikebugs
N can equal 7,8,9,10, or 11?
Well, let's see:

$\displaystyle 10<n+\pi<15$

$\displaystyle 10-\pi<n<15-\pi$

Let's use $\pi\approx3.14$:

$\displaystyle 6.86<n<11.86$

Hence:

$\displaystyle n\in\{7,8,9,10,11\}\quad\checkmark$