Example 3 In a regular $n$-sided pyramid, the range of the dihedral angle 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) $\left(\frac{n-2}{n} \pi, \frac{n-1}{n} \pi\right)$
(1994, National High School Mathematics Competition)
Analysis: When the vertex of a regular pyramid approaches the base infinitely, the dihedral angle between two adjacent sides approaches $\pi$; when the height of the regular pyramid increases infinitely, the dihedral angle approaches an interior angle of a regular $n$-sided polygon, i.e., $\frac{n-2}{n} \pi$. Therefore, the correct choice should be (A).