Miara kąta wewnętrznego $n$-kąta foremnego: $\alpha =\frac{\left(n-2\right)\cdot 180^{\circ }}{n}$

Miara kąta wewnętrznego $\left(n+2\right)$-kąta foremnego: $\beta =\frac{n\cdot 180^{\circ }}{n+2}$

$\alpha =\beta -2^{\circ }$
$\frac{\left(n-2\right)\cdot 180^{\circ }}{n}=\frac{n\cdot 180^{\circ }}{n+2}-2^{\circ }$    $|\cdot n(n+2)$
$180\left(n-2\right)\left(n+2\right)=180\cdot n\cdot n-2\cdot n\left(n+2\right)$
$180\left(n^2-4\right)=180n^2-2\left(n^2+2n\right)$
$180n^2-720=180n^2-2n^2-4n$
$2n^2+4n-720=0$
$\Delta =4^2-4\cdot 2\cdot \left(-720\right)=5776$    $\to$    $\sqrt{\Delta }=76$
$n_1=\frac{-4-76}{2\cdot 2}=-20<0$    $n_2=\frac{-4+76}{2\cdot 2}=18$

Odp.: $n=18$