The inhabitants of planet Rahu measure time in hours and minutes that are…

Concept: On any circular clock dial, each hand sweeps degrees at a constant rate = (total degrees in one full turn) ÷ (time the hand takes for one full turn). The angle between the hour and minute hands at any moment is the difference between the total degrees each hand has swept since the dial's zero position. This works the same way whether the dial uses Earth's 360°/12-hour/60-minute convention or Rahu's stated 720°/36-hour/120-minute-per-hour convention — only the rates change.

Applying to this clock:

1. Find the minute hand's speed: it completes one full 720° turn in 1 Rahuian hour = 120 minutes, so it moves 720 ÷ 120 = 6° every minute.

2. Find the hour hand's speed: it completes one full 720° turn across the whole 36-hour day, so it moves 720 ÷ 36 = 20° every hour, which is 20 ÷ 120 = 1/6° every minute.

3. At 9 hours 48 minutes, the hour hand has swept 9 × 20 + 48 × 1/6 = 180 + 8 = 188°.

4. In the same 48 minutes (within the current hour), the minute hand has swept 48 × 6 = 288°.

5. The angle between the two hands is the difference of these two swept angles: 288° − 188° = 100°.

Cross-check: Measuring by fraction of the day instead — 9 hours 48 minutes is 9 + 48/120 = 9.4 hours out of the 36-hour day, so the hour hand's position is (9.4 ÷ 36) × 720° = 188°, the same value as above. Within the current hour, 48 minutes is 48/120 = 0.4 of an hour, so the minute hand's position measured from the top of that hour is 0.4 × 720° = 288°, again matching. The 100° gap is confirmed independently.

So the angle between the hour hand and the minute hand at 9:48 on this Rahuian clock is 100 degrees.