34*. What is the magnitude of an orthogonal trihedral angle? What is the sum of the magnitudes of polyhedral angles that share a common vertex, have no common internal points, and together cover the entire space?
34. In an orthogonal trihedral angle, the three dihedral angles are right angles, and the sum of their measures is $\frac{3 \pi}{2}$. Subtracting $\pi$ from this, we get $\frac{\pi}{2}$ - the measure of the orthogonal trihedral angle.

Three mutually perpendicular planes divide space into 8 orthogonal trihedral angles. The sum of their measures is $8 \cdot \frac{\pi}{2}=4 \pi$. From additivity, it follows that this will also be the sum of the measures of any polyhedral angles with a common vertex, filling all space.