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# KCC's Quizzes AQQ230 about a clock and angle puzzle

In an analog clock, the angle formed by the hour and the minute hands varies constantly.

Questions:

1. Which angle θ is obtained when it is 5:20 ?
2. Determine when exactly at around 4, the angle will be exactly 90°?

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[edited by: emassa at 1:54 PM (GMT -4) on 29 Mar 2023]
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• 1. θ = 40°

Solution:

θ from 12 for each number = 360° / 12 = 30°

Hour θ movement for each minute = 30° / 60 = 0.5°

For 20 minutes,

number = 4

θ = 4 (30°) = 120°

For 5,

θ = 5 (30°) = 150°

Hour θ movement = 20 (0.5°) = 10°

Total = 150° + 10° = 160°

θ difference = 160° - 120° = 40°

2. 4:05 (minute is 5.45 to be exact)

Solution:

θ from 12 for each number = 360° / 12 = 30°

Hour θ movement for each minute = 30° / 60 = 0.5°

θ for each minute = 360° / 60 = 6°

For 4,

θ = 4 (30°) = 120°

Equation for 90°:

90° = [120° + x (0.5°)] - x (6°)

90° = [120° + 0.5°x] - 6°x

6°x - 0.5°x = 120° - 90°

5.5°x = 30°

x = 5.45

Time would be 4:05 (5.45 to be exact)

• Thanks Mark for your so fast feedback! Rendez-vous next week to compare your answers with the official ones!