Why is the bond angle in an amide ion smaller than the bond angle in a molecule of ammonia?

The nitrogen atom in both NH₃ and NH₂^- has 8 outer shell electrons. In NH₃, 3 pairs of these electrons are used in covalent bonding to hydrogen atoms and the remaining 2 electrons exist as a lone pair. In NH₂, there are 2 lone pairs of electrons due to there only being 2 hydrogen atoms involved in covalent bonding. Lone pairs create a stronger repulsion than bonding pairs. This results in a smaller bond angle in the amide ion due to the increased repulsion due to the extra lone pair. The repulsive force pushes the covalent bonds closer together.