1. (1994 National High School Competition Question) 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. $\left(\frac{n-2}{n} \pi, \frac{n-1}{n} \pi\right)$
1. A. Reason: For a regular $n$-sided pyramid $S-A_{1} A_{2} \cdots A_{n}$ with a fixed regular $n$-sided base, the vertex $S$ moves, and the dihedral angle between adjacent lateral faces is $\angle A_{2} H A_{n}$. When $S$ moves downward approaching the extreme position (i.e., to the center of the base $n$-sided polygon), $\angle A_{2} H A_{n}$ tends to a straight angle; when $S$ moves upward, approaching infinity, the regular $n$-sided pyramid approaches a regular $n$-sided prism, and $\angle A_{2} H A_{n}$ tends to $\angle A_{2} A_{1} A_{n} = \frac{(n-2) \pi}{n}$. Therefore, $\frac{n-2}{n} \pi < \angle A_{2} H A_{n} < \pi$.