Step 1: The dihedral angle in a molecule is the angle between two planes containing different atoms of the molecule.
Step 2: Hydrogen peroxide (H\(_2\)O\(_2\)) has a non-planar structure due to repulsions between lone pairs of oxygen atoms.
- In the gaseous phase, the molecule exists in a skewed conformation with a dihedral angle of 111.5°.
- In the solid phase, due to hydrogen bonding, the dihedral angle is reduced to 90.2°.
Thus, the correct answer is \( 111.5^\circ, 90.2^\circ \).