I stand corrected - serves me right for watching the second hand and not the minute hand on my watch I'm thinking the logic behind your explanation offers the correct solution.its all based on the fact that the hour hand spins at a ratio of 1:12 the speed of the minute hand, so its not like the minute hand actually hits 90 degrees twice every hour.

in 24 hours the hour hand will spin twice, and the minute hand will spin a total of 24. so as it spins round it overtakes the hour hand 22 times. every time it passes it has to make 90 degrees twice in a 360 degree spin so it should be 44 right angles in total. it makes your head go fuzzy picturing it but i figured it out by sitting staring at a picture of a clock for about 10 minutes while a customer was on hold and i was pretending to be investigating a billing issue...