They have to open the carcass to get to the meat. The internal organs are generally eaten first as they are the most nutritious, especially the liver and kidneys. Contrary to what Betty says, predators never eat the stomach contents of their prey - this is merely semi-digested vegetation, which carnivores cannot digest. They often discard the stomach and intestines altogether - they may eat the flesh if they're particularly hungry, but never the contents.

Incidentally, hyenas kill their prey by disembowelling it - the disembowelling is the method of killing, not something that happens after death. Lions, leopards and cheetahs kill their prey by biting its throat until it suffocates, and disembowel it after it is dead.

the underbelly is the easiest entry to the muscle, they eat the liver and sometimes the stomach contents, it sounds revolting but its full of nutrients.