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What is the difference in the degree measures of the angles
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31 Jan 2019, 15:56
31 Jan 2019, 15:56
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What is the difference in the degree measures of the angles formed by the hour hand and the minute hand of a clock at 12:35 and 12:36?
A) 1°
B) 5°
C) 5.5°
D) 6°
E) 30°
A) 1°
B) 5°
C) 5.5°
D) 6°
E) 30°
Re: What is the difference in the degree measures of the angles
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27 May 2019, 12:48
27 May 2019, 12:48
2
Carcass wrote:
What is the difference in the degree measures of the angles formed by the hour hand and the minute hand of a clock at 12:35 and 12:36?
A) 1°
B) 5°
C) 5.5°
D) 6°
E) 30°
A) 1°
B) 5°
C) 5.5°
D) 6°
E) 30°
Difference in minute hands = 1 min = 360/60 = 6 degree
Difference between hour hands = 360/(12*60) = 0.5 degree
So, answer = 6-0.5 = 5.5 degree
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What is the difference in the degree measures of the angles
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15 Feb 2021, 07:11
15 Feb 2021, 07:11
Carcass wrote:
What is the difference in the degree measures of the angles formed by the hour hand and the minute hand of a clock at 12:35 and 12:36?
A) 1°
B) 5°
C) 5.5°
D) 6°
E) 30°
A) 1°
B) 5°
C) 5.5°
D) 6°
E) 30°
Another Approach
Key Points to Remember:
1. Angle moved by Minute hand in 1 min = 6°
2. Angle moved by Hour hand in 1 min = \(\frac{1}{2}\)°
3. Each 5 min sector is 30°
4. Hour hand Angle = \(\frac{Min. hand value}{2}\)
At 12:35
Minute hand is at 35
Hour hand is between 12 and 1
Angle from 12 to 7 (Anti-clockwise) = 5 x 30° = 150°
Angle moved by Hour hand = \(\frac{35°}{2}\) = 17.5°
Total Angle between Hour and Minute hand = 150° + 17.5° = 167.5°
Now, At 12:36
Minute hand is at 36
Hour hand is again between 12 and 1
Angle from 12 to 36 (Anti-clockwise) = 4 x 30° (12 to 8) + 24° (4 minutes, 40 to 36)
Angle moved by Hour hand = \(\frac{36°}{2}\) = 18°
Total Angle between Hour and Minute hand = 120° + 24° + 18° = 162°
So, the difference = 167.5° - 162° = 5.5°
Hence, option C
