Observe that,at any instant,the minute and ho | vedclass

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Question

(A) The angle $	heta$ between the hour hand and the minute hand at $H:M$ is given by the formula $	heta = |30H - 5.5M|$.For $H = 6$ and $M = 15$:$

Vedclass · Accepted Answer

$165$

Vedclass · Answer

(A) The angle $	heta$ between the hour hand and the minute hand at $H:M$ is given by the formula $	heta = |30H - 5.5M|$.For $H = 6$ and $M = 15$:$	heta = |30(6) - 5.5(15)| = |180 - 82.5| = 97.5^{\circ}$.Let the two angles be $\alpha$ and $\beta$. We have $\alpha = 97.5^{\circ}$ and $\alpha + \beta = 360^{\circ}$.Then $\beta = 360^{\circ} - 97.5^{\circ} = 262.5^{\circ}$.The difference between these two angles is $\beta - \alpha = 262.5^{\circ} - 97.5^{\circ} = 165^{\circ}$.

Observe that,at any instant,the minute and hour hands of a clock make two angles between them whose sum is $360^{\circ}$. At $6:15$,the difference between these two angles is $....^{\circ}$.

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