Question

At what time betwwn 5 an 6 minute hand hour hand 180 degrees

Answer 1

we know that,

1minute=6°

30minutes=30×6=180°

Therefore,

At 5:30 the minute hand is 180° between 5 & 6 a.m or p.m

Answer 2

For a complete cycle( 1 circle), hour hand takes 12 hours
360 degree in 12 hours
In 1 hour, hour hand makes 360/12 = 30 degrees
In 1 hour, minute hand moves 360 degrees

In 1 hour, minute hand travels 60 minute spaces
In 1 hour, hour hand travels 5 minute spaces.
Thus in every hour, minute hand gains 55 minutes over hour hand
Now at 5 o' clock:
Difference between hour hand and minute hand = 25 minutes.
The minute hand and our hand are at 180 degree(opposite) at 30 minutes.
Hence minute hand has to gain: 25 + 30 = 55 minutes.

Minute hand gains 55 minute in 60 minutes(every hour)
Hence Exactly at 6 o'clock Hour hand and Minute hand will be 180 degree apart.