Final answer:
The inferior alveolar nerve, a branch of the mandibular nerve, passes through the angle of the mandible and is responsible for providing sensation to the lower teeth and chin. This nerve enters the mandible through the mandibular foramen and exits at the mental foramen.
Step-by-step explanation:
The nerve that passes through the angle of the mandible is the inferior alveolar nerve, which is a branch of the mandibular nerve (V3), itself a division of the trigeminal nerve (cranial nerve V). The mandibular nerve exits the skull through the foramen ovale of the middle cranial fossa and enters the mandible via the mandibular foramen located on the medial side of the ramus of the mandible. From here, the inferior alveolar nerve travels through a tunnel within the mandible, also known as the mandibular canal, and provides sensation to the lower teeth. The nerve emerges at the mental foramen to innervate the skin of the chin.
Anesthesia for dental procedures on the lower teeth is generally administered prior to the point where the inferior alveolar nerve enters the mandibular foramen, which is near the lingula, a small bony projection located close to the mandibular foramen.