1. **State the problem:** Find the obtuse angle between the hour and minute hands of a clock at 11:25 am. 2. **Calculate the minute hand angle:** The minute hand moves 6 degrees per minute. At 25 minutes, the angle from 12 o'clock is $$25 \times 6 = 150^\circ$$. 3. **Calculate the hour hand angle:** The hour hand moves 30 degrees per hour plus 0.5 degrees per minute. At 11:25, the hour hand angle from 12 o'clock is $$11 \times 30 + 25 \times 0.5 = 330 + 12.5 = 342.5^\circ$$. 4. **Find the difference between the two angles:** $$|342.5 - 150| = 192.5^\circ$$. 5. **Determine the obtuse angle:** The smaller angle between hands is $$360 - 192.5 = 167.5^\circ$$, which is obtuse. **Final answer:** The obtuse angle between the hour and minute hands at 11:25 am is $$167.5^\circ$$.