1. In a regular $n$-sided pyramid, the range of the dihedral angle $\alpha$ formed by two adjacent lateral 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) $\left(\frac{n-2}{n} \pi, \frac{n-1}{n} \pi\right)$
Solving for the apex of a regular $n$-sided pyramid lies on a line passing through the center of the base and perpendicular to the base (as shown in the figure), hence there are two extreme positions:

The apex tends to the infinitely far point: $\alpha \rightarrow \alpha_{1}=\frac{n-2}{n} \pi$ (the base angle of a regular prism);
The apex tends to the center of the base: $\alpha \rightarrow \alpha_{2}=\pi$. Therefore, the correct choice is (A).
Taking extremes can also be used to solve certain fill-in-the-blank questions.