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How many times in a day are the hour hand and the minute hand of a wall clock straight (i.e., the angle between them is 180°) ?
Explanation
In a 12-hour period, the hour and minute hands of a clock are opposite (at an angle of 180°) exactly 11 times. While one might expect 12 occurrences, the opposition that would occur between 5:00 and 6:00 and between 6:00 and 7:00 happens at exactly 6:00. This overlap reduces the count by one for every 12-hour cycle.
The hands are 180° apart at approximately these times in a 12-hour cycle:
- 12:32
- 1:38
- 2:43
- 3:49
- 4:54
- 6:00
- 7:05
- 8:10
- 9:16
- 10:21
- 11:27
Since a full day consists of 24 hours, the hands are straight (180°) a total of 11 × 2 = 22 times.
SIMILAR QUESTIONS
The time in the wall-clock is 3.25 the acute angle between the hours-hand and the minutes-hand is
The number of times in a day the Hour-hand and the Minute-hand of a clock at right angles is
How many times are an hour hand and a minute hand of a clock at right angles during their motion from 1.00 p.m. to 10.00 p.m.?
A) 16
B) 18
C) 20
D) 22