Final answer:
The correct geometry for the anti-periplanar arrangement required in the E2 reaction of (CH3)2CHCH2Br with a base is dihedral, not tetrahedral, trigonal planar, or linear.
Step-by-step explanation:
In the E2 reaction of (CH₃)₂CHCH₂Br with a base, the correct geometry for the anti-periplanar arrangement is dihedral. Anti-periplanar geometry refers to a specific three-dimensional arrangement where a hydrogen atom is directly opposite (180° away) to the leaving group (in this case, the bromide ion) across the sigma bond that is being broken. For the E2 mechanism to occur, the C-H and C-Br bonds must be aligned in this way to facilitate the elimination reaction. None of the options such as tetrahedral, trigonal planar, or linear describe this necessary geometric relationship.