Angle between the hands at 4:20

Question

Solve in your head. What is the angle between the hour and minute hands at 4:20? Aim: under 15 seconds.

Accepted Answer

At 4:20 the minute hand is at the 4, i.e. 120^\circ from 12. The hour hand started at the 4 (120^\circ) at 4:00 and has drifted for 20 minutes at 0.5^\circ per minute, so it has moved 20 	imes 0.5 = 10^\circ past the 4: 120^\circ + 10^\circ = 130^\circ. Difference: 130^\circ - 120^\circ = 10^\circ. Formula check: angle = 30H - 5.5M = 30	imes 4 - 5.5	imes 20 = 120 - 110 = 10^\circ. Same. The tempting wrong answer is 0^\circ ("both hands are at the 4"), which ignores that the hour hand has already crept a third of the way toward the 5. Takeaway. Even when the minute hand lands exactly on a n…

Angle between the hands at 4:20

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