Okay, let's tackle this question step by step. The question is about the structure that pierces the investing layer of the deep cervical fascia in the posterior triangle of the neck. First, I need to recall the anatomy of the neck's fascial layers.

The deep cervical fascia has several layers, and the investing layer is the outermost. It covers structures like the sternocleidomastoid and trapezius muscles. In the posterior triangle, the key structures are the accessory nerve (Cranial Nerve XI), the hypoglossal nerve (CN XII), and the vertebral artery.

The investing layer is pierced by certain structures as they pass through. The hypoglossal nerve, which is CN XII, travels from the skull base to the tongue. It would need to pass through the investing layer. The accessory nerve (CN XI) also passes through this area but might be more associated with the sternocleidomastoid. The vertebral artery is in the posterior triangle but is more related to the prevertebral fascia.

The options are not given, but common distractors could include the vagus nerve (CN X), which is in the carotid sheath, or the phrenic nerve, which is in the anterior triangle. The correct answer is likely the hypoglossal nerve (CN XII), which pierces the investing layer in the posterior triangle.

Wait, but I should double-check. The hypoglossal nerve exits the skull through the hypoglossal canal and then travels through the posterior triangle. It does pierce the investing fascia here. The accessory nerve (CN XI) also pierces the investing layer but is more associated with the sternocleidomastoid. So, the hypoglossal nerve is the correct answer here.

The clinical pearl here is that the hypoglossal nerve's course through the posterior triangle and its relationship with the investing fascia is a high-yield point for anatomy exams. Students often confuse the accessory nerve, but it's the hypoglossal that's the key here.

**Core Concept**
The investing layer of the deep cervical fascia encases the sternocleidomastoid and trapezius muscles. In the posterior triangle of the neck, specific neurovascular structures pierce this fascial layer, with the hypoglossal nerve (CN XII) being a critical example due to its anatomical course from the skull base to the tongue.

**Why the Correct Answer is Right**
The hypoglossal nerve (CN XII) exits the skull via the hypoglossal canal, descends through the posterior triangle, and pierces the investing layer of the deep cervical fascia. It innervates all intrinsic and extrinsic tongue muscles except the palatoglossus. Its relationship with the investing fascia is a key landmark in neck anatomy, distinguishing it from other nerves like the accessory nerve (CN XI), which lies deeper.

**Why Each Wrong Option is Incorrect**
**Option A:** The vagus nerve (CN X) is contained within the carotid sheath and does not pierce the investing layer.
**Option B:** The phrenic nerve (C3–C5) traverses the anterior triangle and pierces the prevertebral fascia, not the investing layer.
**Option D:** The

✓ Correct Answer: D. External jugular vein