The bond angle in a molecule decreases with an increasing number of lone pairs due to the greater repulsive forces they exert compared to bonding pairs.

The shape of a molecule and its bond angles are influenced by the repulsion between electron pairs located in the valence shell of the central atom. This phenomenon is described by the Valence Shell Electron Pair Repulsion (VSEPR) theory. According to VSEPR theory, electron pairs arrange themselves in a way that minimizes repulsion and maximizes the distance between them.

Lone pairs of electrons, which do not participate in bonding, occupy more space within the electron cloud surrounding the central atom compared to bonding pairs. This occurs because lone pairs are attracted to only one nucleus, making them more diffuse. Consequently, they exert a stronger repulsive force on adjacent electron pairs, which causes the bonding pairs to be pushed closer together, resulting in a decrease in the bond angle.

For instance, let us examine the molecular structures of water ($\text{H}_2\text{O}$) and ammonia ($\text{NH}_3$). In water, there are two bonding pairs (between the oxygen and hydrogen atoms) and two lone pairs on the oxygen atom. In contrast, ammonia has three bonding pairs (between the nitrogen and hydrogen atoms) and one lone pair on the nitrogen atom. According to VSEPR theory, the bond angle in water is expected to be smaller than that in ammonia due to the higher number of lone pairs. This is confirmed by experimental observations: the bond angle between the hydrogen and oxygen atoms in water is approximately $104.5^\circ$, while the bond angle between the hydrogen and nitrogen atoms in ammonia is approximately $107.3^\circ$.