Based on my readings, valence bond theory (VBT) and molecular orbital theory (MOT) tend to complement one another in explaining a molecule, but I don’t understand how VBT helps us explain the properties of a compound (other than bond angles). How does VBT complement MOT in aiding our understanding of molecules?
You are correct that Valence Bond Theory (VB) is still very active in the chemical bonding community along with MOs. I recommend this article/conversation by Roald Hoffmann about this topic (Acc. Chem. Res. 2003, 36 (10), 750–756). Succinctly, they both are capable of providing a description of bonding in molecules; however, VB theory is better at demonstrating the existence of localized bonds while MO theory is more generalizable to delocalized systems (and ultimately the foundation of predictive computational chemistry). If you have an organic molecule, for example, the VB picture is more helpful for understanding reactivity because these molecules (for some reason) usually behave according to the intuition accessible within such a local bonding framework. MO theory could give you a numerically exact answer, but the wavefunction is in general hard to interpret since it's delocalized across the entire molecule.
One topic that might be of interest to you in this field is MO Localization. This is the field of study which aims to take the MOs and the high accuracy wavefunction and transform them into orbitals that reflect chemistry as intuitively as VB theory. (One can take arbitrary rotations of MOs without changing the observables of the wavefunction). This problem is technically ill-defined, however, there are many approaches that have done this to great success. For example: Natural Bond Orbitals (NBOs), Adaptive Natural Density Partitioning (AdNDP), Intrinsic Bond Orbitals (IAOs), and many others. As the titles suggest, there is a belief that localized (VB-like) bonds are real things hidden in the true wavefunction.