Final answer:
The most critical assessment for a client with acute angina on nitroglycerin is their blood pressure due to the risk of hypotension.
Step-by-step explanation:
The priority assessment for a client diagnosed with acute angina who is receiving an intravenous infusion of nitroglycerin is the client's blood pressure. Nitroglycerin is a potent vasodilator that can cause significant hypotension (low blood pressure), which is a potential adverse effect of the medication. Therefore, monitoring blood pressure is essential to avoid severe hypotension, which can further compromise myocardial oxygen delivery.