The bond angle of an atom is relevant only when it is bonded to two or more atoms, as it measures the angle between those bonds. In the case of carbon dioxide (CO2), the bond angle for carbon is 180 degrees due to its linear structure, while oxygen does not have a defined bond angle since it is only bonded to one atom. The discussion emphasizes that bond angles are typically determined for atoms involved in multiple bonds, and therefore, lone pairs do not contribute to a bond angle measurement for an atom bonded to a single other atom. Additionally, the bond angle in carbon monoxide (CO) is not explicitly stated, but it is implied that similar principles apply regarding the definition of bond angles.