At first sight, the you might think the angle is the difference in angle between the 4 and the 7 on the clock. Since the hours are divided into 12 equal periods of 5 minutes, each 5 minute is equivalent to 360/12=30 degrees. So 7-4=3 equivalent to 90 degrees. But the hour hand has to move between 7 and 8 making the angle bigger than 90 degrees.
360 degrees is equivalent to 2π radians, so 90 degrees is π/2, or about 1.57 radians.
Now we make an adjustment for the movement of the hour hand.
The hour hand moves 30 degrees (π/6 radians) in one hour, so in 20 minutes it moves ⅓ of 30 degrees=10 degrees (π/18 radians). The angle is therefore π/2+π/18=5π/9=1.745 radians approx (100 degrees).