Final answer:
The tarsier is the only living primate that is exclusively carnivorous, feeding primarily on insects and small animals, with distinctive large eyes and head rotation for nocturnal hunting.
Step-by-step explanation:
The only living primate that is exclusively carnivorous is the tarsier. These small, nocturnal primates belong to the family Tarsiidae and are unique among primates in their diet and physiology. While other primates, such as humans, orangutans, monkeys, and apes, are mostly omnivorous, tarsiers feed primarily on insects and sometimes small animals like bats and lizards. Their large eyes and the ability to rotate their heads 360 degrees are adaptations linked to their nocturnal and predatory lifestyle. Unlike other primates, tarsiers cannot manufacture their own Vitamin C and must obtain it from their diet, similar to humans and other haplorrhines.