A set of oxide and chalcogenide tetrahedral glasses are investigated using molecular dynamics simulations. It is shown that unlike stoichiometric selenides such as GeSe$_2$ and SiSe$_2$, germania and silica display large standard deviations in the associated bond angle distributions. Within bond-bending constraints theory, this pattern can be interpreted as a manifestation of {\it {broken}} (i.e. ineffective) oxygen bond-bending constraints. The same analysis reveals that the changes in the Ge composition affects mostly bending around germanium in binary Ge-Se systems, leaving Se-centred bending almost unchanged. In contrast, the corresponding Se twisting (quantified by the dihedral angle) depends on the Ge composition and is reduced when the system becomes rigid. Our results establishes the atomic-scale foundations of the phenomelogical rigidity theory, thereby profoundly extending its significance and impact on the structural description of network glasses.