Final answer:
The affected muscles involved in the patient's symptoms, the masseter and temporalis, are innervated by the trigeminal nerve's mandibular branch (CN V3).
Step-by-step explanation:
The patient's inability to close their mouth and the deviation of the mandible to the left suggests a possible temporomandibular joint (TMJ) disorder or injury following the fall from the bicycle.
Given that the masseter and temporalis muscles are primary muscles involved in closing the mouth (elevation of the mandible), the innervation of these muscles is crucial. The trigeminal nerve, specifically the third branch known as the mandibular branch or CN V3, is responsible for the motor innervation of the muscles of mastication, including the masseter and temporalis.
Therefore, in response to the question, the nerve that innervates the affected muscle, given the symptoms provided, would be CN V3.