Tick Tock Angle

The clock is 360 degrees (it's a circle), 360 / 12 (hours) = 30 degrees for each hour.

The short hand clock does not stop at 12 when its 12:20. 12:(20) is 1/3 of a clock which is 1/3 of a circle or 1/3 of 360 degree.

Thus 12:20 short hour hand is at 1/3 way to 1:00 .

12 to 12:20 is 30 degrees x 4 = 120 - (1/3 x 30) = 120 - 10 = 110

The clock is at 110 degrees when it's 12:20

Angle covered by MINUTE hand in 20 Minutes = $\frac{360}{60}\times20$ = $120^{\circ}$

Angle covered by HOUR hand in 1hour = $\frac {360}{12}\times1$ = $30^{\circ}$

Angle covered by HOUR hand in 20 Minutes = $\frac{30}{60}\times20$ = $10^{\circ}$

Therefore, smaller angle formed by the hour hand and the minute hand of a clock at 12:20 = $120^{\circ}$ - $10^{\circ}$ = $110^{\circ}$

I actually did it somewhat differently.....

If the hour hand did not move and stayed at the "12" position even at 12:20, the minute hand would (still) be at the "4" position and thus the angle would be 4 spaces, or 4/12, or 120 degrees.

However, since the hour hand does move, we know that the angle must be less than 120; thus, we can rule out the choices "120" and "130".

Since the hour hand moves 1/12 of the clock per hour, and 20 minutes (the 20 part of 12:20) is 20/60 of an hour, or 1/3, we do $\frac{1}{3} \times \frac{1}{12} = \frac{1}{36} = \frac{10}{360} = 10$ degrees.

Since the answer must be less than 120, it must be $120 - 10 = \boxed{110}$

First calculate the angle between the minute hand and 12 'o' clock which comes to 120 degrees. Then, the angle made by the hour hand with 12 'o'clock comes to = (20/60x12) x 360 = 10 degrees. So the angle will be = 120-10 = 110 degrees

Para encontrar o ângulo entre os ponteiros do relógio podemos usar a seguinte fórmula: | 11m - 60h | /2 , onde m são os minutos e h são as horas. Substituindo os valores na fórmula temos: | 11.20 - 60.12| /2 = 250. Como queremos saber o menor ângulo bastar subtrair 250 de 360, que é igual a 110

Just by analyzing the clock, from 12 to 4 the angle between the hour hand and minute is equal to 120 degrees ( since the circle is divided equally into 12 spaces and the angle between spaces is 30 degrees.) At 12:20 the hour hand theoritically will travel (20/60)x30 = 10 degrees.. therefore from the figure the angle required is 120 - 10 = 110 degrees..

The formula for angle between two hands of a clock = ø = 30h – 11/2 m when minute hand is behind the hour hand or ø = 11/2 m – 30 h when it is ahead of hour hand. where h is hours completed and m is minutes completed.

at 12 O'clock h = 0 and m = 20 so a 12:20 ø = 11/2 m – 30h = 11/2 × 20 – 0 = 110°

for (12+20/60)hr angle traced by hour hand is (360/12)*(12+20/60)=370 degrees

Angle traced by mint hand in 20 min is (360/60)*20=120 degrees.

==>angle difference between them is 370-120=250 degrees.

but the min angle between them is 360-250=110 degrees

The hour hand goes exactly 1/12 times slower than the minute hand (that's why hour hand moves just a round while minute hand completes 12 round). a full round= 360 degree i.e. a minute step= 360/60=6 deg

  the  minute hand is at 20 min.
 from 12 o clock it has moved 6*20=120 deg.
  Meanwhile, the hour hand has moved from 12 o clock 120/12=10 deg.
   i.e. the angle between them= 120-10 deg=110 deg

for every 10min there wil be a increase in 5 degree in hour hand. similarly wen 12.20. 12- 20 wil be 120 degree but the hour hand moves 10 degree so the value wil be 110 degree....