The angle between the minute hand and the hour hand of a clock when the time is 4.20 is

10°

At 4 O'clock, Minute hand is at 12 while the Hour hand is at 4. Again the minute hand has to sweep through ( 30 x 4 ) ie 120 degrees for reaching the figure 4 to show 20 mins. We can write 4 hrs. 20 mins. as \(\frac{13}{3}\) hrs. Angle traced by hour hand in \(\frac{13}{3}\) hrs =30× 13/3=130 degrees

Angles between hands of clock =130 degrees −120 degrees=10 degrees.