11.3. The Pyramid of Khufu has a square base, and its lateral faces are equal isosceles triangles. Can the angle of the face at the apex of the pyramid be equal to $95^{\circ} ?$
Answer: No, it cannot.

Solution.

The lateral surface of the pyramid consists of four equal isosceles triangles. If we cut the lateral surface of the pyramid along the lateral edges and unfold it onto a plane, we will get the figure shown in Fig. 1. In this case, the common point of the triangles is the vertex of the pyramid. If the angle of the face at the vertex of the pyramid were $95^{\circ}$, then the sum of the four angles would be $380^{\circ}$. This is impossible, as the sum of the angles at the vertex of the pyramid is less than $360^{\circ}$ (this is evident from Fig. 1).

![](https://cdn.mathpix.com/cropped/2024_05_06_5b4358c55580fc5d6afcg-2.jpg?height=385&width=371&top_left_y=370&top_left_x=794)

Fig. 1

Comment. A correct answer without justification - 0 points.