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It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.

  1. $0^{\circ}$
  2. $7.5^{\circ}$
  3. $15^{\circ}$
  4. $22.5^{\circ}$
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Method Ⅰ

ϴ = 30H – $\frac{11M}{2}$

i.e. 30(3) - $\frac{11(15)}{2}$

= 90 – 82.5 = $7.5^{\circ}$

 

Method  II

1 H = $\frac{360}{12}$ = $30^{\circ}$

15 Min = $\frac{1}{4}$H = $\frac{30^{\circ}}{4}$ = $7.5^{\circ}$

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