Final answer:
The a) axillary nerve is the most commonly injured nerve in anterior shoulder dislocations due to its location near the shoulder joint capsule.
Step-by-step explanation:
The most commonly injured nerve in anterior shoulder dislocations is the axillary nerve. This type of dislocation typically occurs when force is applied to the humerus with the arm in an abducted position, such as when one falls on an outstretched hand or elbow. Anterior dislocations can affect the axillary nerve due to its proximity to the inferior part of the capsule of the shoulder joint, where it travels through the quadrangular space with the posterior circumflex humeral artery to innervate the deltoid and teres minor muscles, and provide sensation to the skin over a part of the deltoid.