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

10°

The minute hand moves $6^\circ$ every minute.

At 20 minutes:

$\text{Minute hand position} = 20 \times 6^\circ = 120^\circ$

The hour hand moves $30^\circ$ for every hour, plus an extra $0.5^\circ$ for every passing minute.

At 4 hours and 20 minutes:

$\text{Hour hand position} = (4 \times 30^\circ) + (20 \times 0.5^\circ)$

$\text{Hour hand position} = 120^\circ + 10^\circ = 130^\circ$

$\text{Angle} = \vert{}130^\circ - 120^\circ\vert{} = 10^\circ$