2. Is it true that in three-dimensional space, two angles with respectively perpendicular sides are either equal or sum up to $180^{\circ}$?
Solution. Consider, for example, the cube $A B C D A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ (see figure). The angles $A B C$ and $B C^{\{\prime\}} C$ satisfy the condition, since $A B \perp B C^{\{\prime\}}$ (by the theorem of three perpendiculars) and $B C \perp C^{\{\prime\}} C$. In this case, the angle $A B C$ is a right angle, and the angle $B C^{\{\prime\}} C$ is $45^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_bf2fa7e43c9ea5c20268g-1.jpg?height=399&width=500&top_left_y=1391&top_left_x=778)

Answer: incorrect.

Remarks. Of course, there are other examples.