Final answer:
The vertebral artery, which branches from the left subclavian artery, is responsible for carrying blood to the brain.
Step-by-step explanation:
The branch of the left subclavian artery that carries blood to the brain is the vertebral artery. The vertebral artery branches from the subclavian artery and passes through the transverse foramen in the cervical vertebrae, entering the base of the skull at the vertebral foramen.
Meanwhile, the internal carotid artery and external carotid artery are branches of the common carotid artery and not the subclavian artery. The brachiocephalic artery is distinct in that it is located only on the right side of the body, branching into the right subclavian artery and the right common carotid artery. The left subclavian artery, which arises from the aortic arch, primarily supplies blood to structures like the arms, chest, shoulders, back, and parts of the central nervous system, with the vertebral artery being responsible for supplying the brain.