At what time between 4 and 5 o’clock will the hands of a clock be at right angle.

The hands of a clock form a right angle (90 degrees) twice in every hour.

To find the times between 4 and 5 o'clock when the hands are at a right angle, we need to understand that the minute hand moves 12 times faster than the hour hand.

At 4 o'clock, the hour hand is at 4 and the minute hand is at 12. The minute hand will catch up to the hour hand at a right angle in two instances:

1. When the minute hand is at 3 (15 minutes past the hour), the hour hand will be 1/4 of the way between 4 and 5. This is because the hour hand moves to the next hour every 60 minutes, so in 15 minutes it will have moved 1/4 of the distance.

2. The second time the hands form a right angle is a little trickier to calculate. The minute hand will have to make almost a full revolution and catch up to the hour hand from behind. This happens 3/4 of the way through the hour, or 45 minutes past the hour. At this time, the minute hand is on the 9 and the hour hand is 3/4 of the way between 4 and 5.

So, the hands of the clock are at right angles at approximately 4:15 and 4:45.