Question

How many times do the hands of a clock make 90° angle in a day?​

Answer 1

If you switch to a rotating coordinate system in which the hour hand stands still, then the minute hand makes only 11 revolutions, and so it is at right angles with the hour hand 22 times. In a 24 hour day you get 2×22=44.

Answer 2

In other words, the minute hand "overtakes" the hour hand on 44 occasions in 24 hours in order to give a 90 degree angle. Therefore the answer to your question is 44. Each hour has 2 occurrences of 90 degrees. In 12 hrs, it overtakes 24 times.

I hope it helps you mate ✨