Question

What is the larger angle between the minute hand and hour hand at 12:40?​

Answer 1

The answer is 140 degrees

At 12:00 the angle is 0 degree

At 12:40 the angle between 12:00 and minute hand=30*8=240 degree

this is because angle covered by minute hand in 5 minutes is 30 degree

At 12:40 the angle between 12:00 and hour hand=40*1/2=20 degree

his is because angle covered by hour hand in 1 minute is 1/2 degree

Now,the angle between hour hand and minute hand=240–20=220 degree

if taken obtuse angle=360-220=140 degrees

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Answer 2

Given : 12:40 time

To find : larger angle between the minute hand and hour hand

Solution:

Hour hand in 12 hrs = 360°

Hour hand in 1 hr  (60 minutes) = 360/12 = 30°

Hour hand in 1 minute  = 30/60 = 0.5°

Minute hand in 1 hr  (60 minutes) = 360°

Minute hand in 1 minute  = 360/60 = 6°

in 40 Minutes , Minute hand = 6 * 40 = 240°

Hour hand in 40 minute  = 40 x 0.5°  = 20°

angle between the minute hand and hour hand at 12:40 = 240 - 20 = 220°

other angle = 360° - 220° = 140°

220° > 140°

larger angle between the minute hand and hour hand at 12:40 is 140°

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