Step 1: Understanding the Concept
Peptide hormones are water-soluble and cannot cross the plasma membrane, so they bind receptors on the cell surface.
Step 2: Signalling
The hormone-receptor complex activates a G-protein, which switches on the enzyme adenylate cyclase. This enzyme converts ATP into cyclic AMP, the second messenger.
Step 3: Why the other options fail
Carbonic anhydrase, alkaline phosphatase and cholinesterase are not part of this hormone signalling pathway.
Final Answer:
The enzyme is adenylate cyclase.
\[ \boxed{\text{(A) }\text{adenylate cyclase}} \]