Final answer:
Bile is transported from the gallbladder to the duodenum via the common bile duct, which is crucial for fat digestion.
Step-by-step explanation:
Bile empties into the duodenum through the common bile duct, a structure formed by the union of the common hepatic duct and the gallbladder's cystic duct. This duct allows the bile produced in the liver to be stored in the gallbladder or released into the duodenum, where it plays a critical role in the digestion and absorption of fats. Specifically, in the duodenum, bile emulsifies fats, aiding in their digestion by the enzyme lipase, and facilitating the absorption of fat-soluble vitamins such as vitamin K.