##### CLOCK-ANGLES

- The angle between hours and minutes for a given time x:y(x hours and y minutes) is |30*x-11*y/2|(absolute value)

this comes from the fact that a hour hand elapses 30 degrees for every hour(360/12) and minute hand elapses 6 degrees(360/60)..but for 6:50,the hour hand also elapses extra offset from its original position where it has to be there at 6:00 sharp..the offset is calculated as follows:

1.for every 60 minutes of minutes hand,hour hand elapses 1 hour..so distance travelled by hour hand when the minute hand travels 1 min is 1/60

2.so the offset is (50/60)*30 degrees for the hour hand

3.so the total angle covered by hour hand for 6:50 is 6*30 degrees+offset=180+25=205 degrees

4.angle covered by minute hand is 50*6 degrees=300 degrees

So,angle between them =300-205=95 degrees )

If **θ degrees is the angle between minutes and hours clock,then**

**θ= |30*x-11*y/2| where,y=minutes elapsed and x=hours elapsed**

- Hours hand rotates 30 degrees in a hour
- Minutes hand rotate 6 degrees per minute
- Hours hand rotate 0.5 degree in a minute
- If the answer we get through the above process is not found in given answers then find 360-(answer we get).
- If
**θ is the angle we get from the process then its reflective angle is found by 360- θ.** - If the hours hand and minutes hand are in straight line then the angle between them=180 degrees
- If the hours hand and minutes hand are together then the angle between them=0 degrees
- If we are unable to find the exact angle try to find

**θ= 30*H-5.5*M** and **θ= 5.5*M -30*H**

We can see any of the answer obtainted in given options

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

#### At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?

#### What is the angle between the minute and the hour hand of the clock which shows 12:24?

#### The reflex angle between the hands of a clock at 10.25 is:

#### A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

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