[67 \dfrac{1}{2}^\circ] At what angle the hands of a clock are inclined at 15 minutes past 5?

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At what angle the hands of a clock are inclined at 15 minutes past 5?

58$ \dfrac{1}{2} ^\circ $

64$^\circ$

67$ \dfrac{1}{2}^\circ $

72$ \dfrac{1}{2} ^\circ $

Explanation:

Angle traced by hour hand in$ \dfrac{21}{4} $hrs =$\dfrac{360}{12}\times\dfrac{21}{4} ^\circ $=157$ \dfrac{1}{2} ^\circ $

Angle traced by min. hand in 15 min. =$ \left(\dfrac{360}{60} \times 15\right)^\circ $= 90$^\circ$.

$\therefore$ Required angle =$ \left(157\dfrac{1}{2} \right)^\circ $- 90$^\circ$ = 67$ \dfrac{1}{2} ^\circ $

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