35. If rays are drawn from the center of a cube to its vertices, these rays can be considered as the edges of six tetrahedral angles into which the entire space is divided. Calculate the magnitudes of the planar and dihedral angles of these tetrahedral angles.
35. Six congruent four-sided angles fill all space. Therefore, the magnitude of each of them is $\frac{4 \pi}{6}=\frac{2 \pi}{3}$. This magnitude is obtained by subtracting the number $2 \pi$ (the sum of the angles of a square) from the sum of the magnitudes of the dihedral angles. This sum is $\frac{2 \pi}{3}+2 \pi=\frac{8 \pi}{3}$, and the magnitude of each dihedral angle, therefore, is $\frac{\pi}{3}$, or $120^{\circ}$. The plane angles of these four-sided angles are the plane angles between the diagonals of the diagonal sections of a cube. The tangent of the angle between the diagonal and the larger side of such a section is $\frac{1}{\sqrt{2}}$, the angle itself is approximately $35^{\circ} 15^{\prime} 52^{\prime \prime}$, and the angle between the diagonals is twice as large, i.e., approximately $70^{\circ} 31^{\prime} 44^{\prime \prime}$.