Final answer:
The molecular geometry at the central atom in CH2Br2 is tetrahedral, based on VSEPR theory which states that four bonding pairs around the central atom result in a tetrahedral shape to minimize electron pair repulsion.
Step-by-step explanation:
The molecular geometry at the central atom in CH2Br2 is tetrahedral. This can be explained by considering that the molecule has a total of four atoms bonded to the central carbon atom with no lone pairs on the carbon. According to VSEPR theory, when there are four bonding pairs, the electron pair geometry is tetrahedral, and consequently, the molecular geometry is also tetrahedral. This shape provides the most separation between the electron pairs, which minimizes their repulsion according to VSEPR theory. The bond angles in a tetrahedral geometry are approximately 109.5°.