Final answer:
Hox genes are a cluster of genes responsible for determining the body plan in animals. The gene regulating branchial arch IV inter-arch identity is Hoxa2.
Step-by-step explanation:
Hox genes are a cluster of genes responsible for determining the general body plan, including the number of body segments and the placement of appendages, in animals. They encode protein transcription factors that control the expression of numerous other genes during embryonic development. Hox genes are homologous across the animal kingdom and are expressed in certain body segments at certain stages of development. In the context of the provided options, the gene regulating branchial arch IV inter-arch identity is Option 3: Hoxa2.