Final answer:
For a patient with acute hypercapnic respiratory failure due to muscle fatigue, options II (continuous positive airway pressure) and IV (bilevel pressure support by mask) would be appropriate.
Step-by-step explanation:
A patient who develops acute hypercapnic respiratory failure due to muscle fatigue may require ventilatory support. In this case, options II (continuous positive airway pressure) and IV (bilevel pressure support by mask) would be considered. Continuous positive airway pressure (CPAP) provides a constant level of pressure throughout the respiratory cycle, which helps keep the patient's airways open and improves oxygenation. Bilevel pressure support provides two levels of pressure, higher during inspiration and lower during expiration, to assist with breathing in patients experiencing respiratory failure.