$22 \cdot 10$ A line $l$ intersects with the two half-planes of a right dihedral angle, and the angles formed with these two half-planes are $\alpha$ and $\beta$. Then the value that $\alpha+\beta$ must not take is
(A) $90^{\circ}$.
(B) $73^{\circ}$.
(C) $87^{\circ}$.
(D) $95^{\circ}$.
(High School Mathematics Competition in Beijing, China, 1990)
[Solution] As shown in the figure, $B C \perp P Q, A D \perp P Q$. Connect $A C, B D$, then $\angle C A B, \angle A B D$ are the angles $\alpha, \beta$ between line $l$ and planes $M$ and $N$, respectively. The lengths of the other line segments are set as shown in the figure.

Then $\sin \alpha=\frac{d}{e}, \cos \alpha=\frac{b}{e}, \sin \beta=\frac{a}{e}, \cos \beta=\frac{c}{e}$. By $\cos (\alpha+\beta)=\cos \alpha \cos \beta-\sin \alpha \sin \beta$
$$
=\frac{b c}{e^{2}}-\frac{a d}{e^{2}}=\frac{b c-a d}{e^{2}},
$$

In Rt $\triangle A C D$ and Rt $\triangle B C D$,
$$
a0$, then $\alpha+\beta<90^{\circ}$.
Therefore, $\alpha+\beta$ cannot be $95^{\circ}$.
Hence, the answer is $(D)$.