twice if you're looking for exact right angles
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44 times. Starting at 12 o'clock, over the next 12 hours, the hour hand will make a 90o angle to the right (like quarter past) 11 times and 90o angle to the left (like quarter to) making a total of 22 times per 12 hours, or 44 per 24 hours aka 1 day.
Twice in a 24 hour cycle at 3:00.
44 times in 24 hours.(Considering the hour- and minute-hands only.)
The second hand on the clock circles 420 times in 7 hours.
3:00 am, 3:00 pm, 9:00 am, 9:00 pm