Final answer:
The branches of the trigeminal nerve exit the skull through the stylomastoid foramen, foramen ovale, and foramen spinosum.
Step-by-step explanation:
The branches of the trigeminal nerve exit the skull through several openings. One point of exit is the stylomastoid foramen, which is located between the styloid process and mastoid process and serves as the exit point for the cranial nerve that supplies the facial muscles.
Another point of exit is the foramen ovale of the middle cranial fossa, which provides passage for a major sensory nerve to the lateral head, cheek, chin, and lower teeth. Lastly, the trigeminal nerve also exits the skull through the foramen spinosum, a small opening located posterior-lateral to the foramen ovale, serving as the entry point for an important artery that supplies the covering layers surrounding the brain.