Find the angle between the hour-hand and minute-hand in circular measure at 4 O' clock.

Solution

We know that

 1 revolution = 360° .............................(i)

for hour-hand,

∵ hour-hand in 12 hour rotation= 1 revolution

 ∴ ...................1 hour hour rotation =1/12 revolution

 ∴ ...................4 hour hour rotation =4/12 revolution=1/3 revolution

from (i), 1 revolution = 360°

              1/3 revolution=360° × 1/3 =120°

for minute-hand ,

∵minute-hand in 60 minute rotation =1 revolution

 ∴ ...................1minute rotation= 1/60 revolution

 ∴ ................... zero minuite rotation = 0 × 1/60 revolution =0 revolution

from(i),1 revolution = 360° 

             0 revolution= 360° × 0=0°

angle between the hour-hand and minute-hand in circular measure at 4 O' clock

= 120° - 0° 

= 120° answer