Final answer:
The palatoglossus muscle is the extrinsic tongue muscle innervated by the vagus nerve (CN X). Other extrinsic muscles like hyoglossus, styloglossus, and genioglossus are innervated by the hypoglossal nerve (CN XII).
Step-by-step explanation:
The extrinsic muscle of the tongue that is innervated by cranial nerve X (vagus nerve) is the palatoglossus muscle. This muscle originates on the soft palate and its main function is to elevate the back of the tongue during swallowing and speech.
The vagus nerve plays a vital role in controlling this muscle, making it unique among the extrinsic tongue muscles, which are typically innervated by the hypoglossal nerve (CN XII).
Other extrinsic muscles include the hyoglossus, which depresses and retracts the tongue; the styloglossus, which elevates and retracts the tongue; and the genioglossus, responsible for protruding the tongue. Understanding the innervation of these muscles is crucial for diagnosing and treating conditions that affect speech and swallowing.