Kabir notices the angle between the hands at the time shown. After how many minutes will the hands next make exactly the same angle?

At 2:30 the hour hand is at 75° and the minute hand at 180°, so the minute hand leads by 105°. The same angle comes back when it leads by 360 − 105 = 255°: (255 − 105) ÷ 5.5 = 150/5.5 = 27 3/11 min. (65 5/11 min is the gap between overlaps.)