Question

What is the angle between the minute hand and the hour hand of a clock when the clock shows 3 hours 20 minutes?

Answer 1

The angle between the minute hand and the hour hand at three o'clock is ${90}^o$.

For a minute, the hour hand rotates by $30/60=1/2$ degrees.

In $1$ minute, the angle changes by ${5.5}^o$

In $20$ minutes, the angle changes by $5.5\times 20={110}^o$.

Therefore, the angle between the two hands at $3:20$ $={110}^o-{90}^o={20}^o$