Final answer:
A priority nursing responsibility would be to have oxygen available.
Step-by-step explanation:
A priority nursing responsibility when examining the throat of a child diagnosed with acute epiglottis would be to have oxygen available. Acute epiglottis is a potentially life-threatening condition that causes swelling of the epiglottis, a flap that covers the entrance to the larynx. This swelling can obstruct the airway and lead to respiratory distress. Having oxygen available ensures that the child can receive adequate oxygenation while further interventions are initiated.