Final answer:
The modifiable risk factor for stroke that a nurse should teach a patient about is hypertension, which can be managed through medications and lifestyle changes.
Step-by-step explanation:
The nurse should teach the patient that hypertension is a modifiable risk factor for stroke. Age, gender, and family history are not modifiable risk factors. Hypertension, on the other hand, can often be controlled with medications and lifestyle changes such as improving nutrition, increasing physical activity, maintaining a healthy weight, and avoiding tobacco use. These actions can help keep blood pressure within a normal range and significantly reduce the risk of a stroke.