The vertebral artery passes through the transverse foramina of the cervical vertebrae. The alar ligament connects the odontoid process of cervical vertebra 2 (C2), also known as the axis, to the occipital bone. The nuchal ligament spans from the external occipital protuberance to the spinous process of C7. Although the internal and external carotid arteries supply blood to structures in the cervical spine, the do not pass through the transverse foramina.

The five major branches of the facial nerve are (in order from superior to inferior): Temporal, Zygomatic, Buccal, Marginal mandibular, and Cervical. (A helpful mnemonic: The Zebra Bit My Cookie)

Distal to the stylomastoid foramen (extracranially) the facial nerve also branches to the digastric muscle as well as the stylohyoid muscle. The facial nerve also gives off a branch to the posterior auricular nerve which controls scalp muscles around the ear.

The pulmonary artery carries oxygen-poor blood from the right ventricle to the lungs. The blood here passes through capillaries adjacent to alveoli and becomes oxygenated as part of the process of respiration. The oxygen-rich blood then enters the pulmonary vein and is drained into the left atrium of the heart. From the left atrium blood then enters the left ventricle where it will be ejected through the aorta. 

In contrast to the pulmonary arteries, the bronchial arteries supply nutrition to the lung themselves. The peroneal vein (aka fibular vein) helps carry blood from the lateral compartment of the leg.

The axillary nerve, along with the posterior circumflex humeral artery and vein, pass through the quadrangular space. The quadrangular space boundaries consist of the teres minor muscle, the surgical neck of the humerus, the superior margin of the teres major, and the long head of the triceps brachii.

The long thoracic nerve innervates the serratus anterior, and only has motor function. Although the musculocutaneous nerve provides cutaneous sensation to the lateral forearm, it also innervates the biceps brachii, brachialis, and coracobrachialis muscles. The tibial nerve innervates the hamstrings (except the biceps femoris short head) and provides sensation to the plantar surface of the foot (via the plantar nerves). The saphenous nerve provides cutaneous sensation to the medial lower extremity, and does not have any motor function

The celiac trunk (which comes off the abdominal aorta) divides into the splenic, common hepatic, and left gastric arteries. The splenic artery, is large and highly tortuous. It gives off the left gastroepiploic artery, some short gastric arteries, and some pancreatic branches. The common hepatic artery, gives off the proper hepatic artery, the right gastric artery, and the gastroduodenal artery. The left gastric artery gives rise to the esophageal and hepatic branches.

The gastroduodenal artery branches from the common hepatic artery where it descends behind the duodenum to divide into the right gastroepiploic and superior pancrearicoduodenal arteries.

The femoral triangle contains (from lateral to medial) the femoral nerve, artery, vein, and canal. The pulsation of the femoral artery may be felt just inferior to the midpoint of the inguinal ligament.

The femoral triangle is bounded by the inguinal ligament superiorly, the sartorius muscle laterally, and the adductor longus muscle medially. The floor of the femoral triangle is formed by the illiopsoas, pectineus, and adductor longus muscles. 

The Vagus nerve has both sensory and motor function. The sympathetic and parasympathetic nervous systems are responsible for the "fight or flight" and "rest and digest" actions of the autonomic nervous system respectively. The Vagus nerve is responsible for the parasympathetic motor nerves.

The question is asking for a sensory nerve, meaning we can eliminate the trochlear and hypoglossal nerves. The olfactory nerve is responsible for smell whereas the optic nerve for vision, making the correct answer the optic nerve.

There are only four cranial nerves with both sensory and motor functions: the trigeminal, facial, glossopharyngeal, and vagus nerves. Only two of those are answer choices: facial and trigeminal. While the facial nerve controls the tongue, only the trigeminal nerve is responsible for the muscles of mastication around the mouth, making the trigeminal nerve the correct answer.