Final answer:
The atlanto-occipital joint is responsible for the highest degree of mobility in the neck, allowing a normal head extension of up to 35 degrees.
Step-by-step explanation:
The joint that provides the highest degree of mobility in the neck, with a normal head extension of up to 35 degrees, is the atlanto-occipital joint. This articulation consists of the superior articular processes of the atlas and the occipital condyles at the base of the skull. The atlanto-occipital joint enables considerable extension, flexion, and lateral flexion movements, facilitating the head's up and down motion, comparable to saying "yes". By contrast, the atlantoaxial joint allows for the rotation of the head, such as when shaking your head "no".