Question

write any time in the clock when angle measure between the hour hand and the minute hand of the clock is 20 degrees

Answer 1

One time will be

3 minutes 30 seconds past 10

Step-by-step explanation:

In a clock

The minute hand rotates 360° in 1 hour (60 minutes)

Therefore, the minute hand will rotate in 1 minute = 6°

Similarly, the hour hand will rotate in 1 minute = 360/(12 × 60) = 1/2°

Let in x minutes the angle between hour and minute hand is 20°

Therefore,

$\frac6x-\frac{x}{2}=20$

$\implies \frac{11x}{2}=20$

$\implies x=\frac{40}{11}$

$\implies x=3\frac{7}{11}$ minutes

or $x= 3\text{ minutes} 30\text{ seconds}$ (Approx)

Thus, if clock is showing 10:3:30 time or 3 minutes 30 seconds past 10 o'clock then the angle between hour hand and minute hand will be 20°

Hope this answer is helpful.

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