[ Measurement of segment lengths and angles. Adjacent angles.]

How many times in a day do the hour and minute hands coincide? Form a straight angle? Form a right angle?
In a day, the minute hand makes 24 revolutions, while the hour hand makes 2. Therefore, the minute hand overtakes the hour hand 22 times. At the moment of overtaking, they coincide. (In this case, one midnight is counted, but the second one is not.)

The moments of coincidence of the hands divide the day into 22 equal segments. On each such segment, the hands form a straight angle once and are perpendicular twice (when the minute hand is ahead and when it is behind the hour hand by $\left.90^{\circ}\right)$.

## Answer

22 times, 22 times, 44 times.