The problem is about determining the bond angle values in a fac-\(\left[ Co\left( NH _3\right)_3 Cl _3\right]\) complex. This is a coordination complex with cobalt as the central metal atom coordinated with three ammonia \((\text{NH}_3)\) and three chloride ions \((\text{Cl}^-)\).
In coordination chemistry, complexes can form different geometries based on their coordination number and the type of ligands. For a fac-\(\left[ Co\left( NH _3\right)_3 Cl _3\right]\), we focus on the geometry of the face isomer.
The fac (facial) isomer of a \(ML_3L'_3\) complex typically forms an octahedral geometry. In an octahedral complex:
In this context, the \(Cl - Co - Cl\) bond angles refer to angles between the chloride ion ligands and the central cobalt, which in a fac isomer are located on the same face. Therefore, the bond angles between these chloride ligands are indeed \(90^{\circ}\).
Thus, the correct answer for the \(Cl - Co - Cl\) bond angle in the fac-\(\left[ Co \left( NH _3\right)_3 Cl _3\right]\) complex is:
90°