Question

In a clock, the hour hand is at 6, the minute hand at 12 and the second hand somewhere between 8 and 9. If the angle made by second hand and hour hand is 73${}^{\circ }$, what is the angle(in degrees) between the minute hand and second hand?

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Answer 1

Let us name the hour hand A, the minute hand B, the second hand C and the center of the clock as O.

The minute hand and the hour hand form a straight angle.
Therefore, $\angle$AOB = 180^o

$\angle$AOC + $\angle$COB = 180${}^{\circ }$ (linear pair axiom)

$\angle$COB = 180${}^{\circ }$ - 73${}^{\circ }$ = 107${}^{\circ }$

Therefore, the angle between the minute hand and the second hand, i.e. $\angle$COB, is 107${}^{\circ }$.