In a regular $n$-sided pyramid, the range of the dihedral angle formed by two adjacent side faces is ( ).
(A) $\left(\frac{n-2}{n} \pi, \pi\right)$
(B) $\left(\frac{n-1}{n} \pi, \pi\right)$
(C) $\left(0, \frac{\pi}{2}\right)$
(D) $\left(\frac{n-2}{n} \pi, \frac{n-1}{n} \pi\right)$
Consider extreme cases. As shown in the figure, let the center of the base of the regular $n$-sided pyramid $S A_{1} A_{2} \cdots A_{n}$ be $O$. Without loss of generality, let the base of the $n$-sided pyramid be fixed, and let the vertex move along the line of the pyramid's height $SO$. The dihedral angle between two adjacent lateral faces is $\angle A_{2} H A_{n}$. When $S$ approaches $O$ infinitely, $\angle A_{2} H A_{n}$ tends to a straight angle; and when $S$ moves infinitely far from $O$, $H$ approaches point $A_{1}$, i.e., $\angle A_{2} H A_{n}$ approaches $\angle A_{2} A_{1} A_{n}$, and $\angle A_{2} A_{1} A_{n}=\frac{(n-2) \pi}{n}$. In summary, $\angle A_{2} H A_{n} \in\left(\frac{(n-2) \pi}{n}, \pi\right)$. Therefore, the answer is $\Lambda$.