**Core Concept**
The glossopharyngeal nerve (cranial nerve IX) supplies the posterior part of the tongue due to its embryological origin. During embryonic development, the tongue is formed by the fusion of the first pharyngeal arch (mandibular arch) and the third pharyngeal arch (also known as the third branchial arch). The glossopharyngeal nerve, which arises from the third pharyngeal arch, innervates the posterior one-third of the tongue.

**Why the Correct Answer is Right**
The posterior part of the tongue is primarily responsible for taste and swallowing functions. The glossopharyngeal nerve conveys taste sensations from the posterior one-third of the tongue to the solitary nucleus in the medulla oblongata. Additionally, it provides motor innervation to the stylopharyngeus muscle, which aids in swallowing. The development of the glossopharyngeal nerve from the third pharyngeal arch explains its association with the posterior part of the tongue.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the hypoglossal nerve (cranial nerve XII) is responsible for motor innervation of the tongue, but not its sensory innervation.
* **Option B:** This option is incorrect because the facial nerve (cranial nerve VII) primarily supplies the anterior two-thirds of the tongue with taste fibers, not the posterior part.
* **Option D:** This option is incorrect because the vagus nerve (cranial nerve X) supplies the epiglottis and the pharynx, but not the posterior part of the tongue.

**Clinical Pearl / High-Yield Fact**
The embryological origin of the glossopharyngeal nerve from the third pharyngeal arch explains its association with the posterior part of the tongue, which is primarily responsible for taste and swallowing functions.

**Correct Answer:** C