Final answer:
The α-helix is the protein secondary structure known for being highly extensible due to its coiled nature.
Step-by-step explanation:
The type of protein secondary structure that is characterized as being highly extensible because of its coiled structure is the α-helix. The α-helix is a common secondary structure in proteins, where the polypeptide chain folds into a helix shape stabilized by hydrogen bonds. It is known for its elasticity due to the coiling, which allows it to be extended or compressed. Other secondary structures include β-pleated sheets, which are important in structural proteins like silk fibroin but are not highly extensible like the α-helix. Additionally, random coils and triple helix structures can be found within the secondary structure of proteins, but they do not share the same extensible properties as the α-helix.