angle in the given time

Geometry Level 1

Find the smaller angle in degrees formed between the hour hand and the minute hand at exactly 3 : 40 3:40 .

Note: The red color is the hour hand and the yellow color is the minute hand.

110 130 70 210

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1 solution

With reference to 12 12 , the hour hand travels 0. 5 ∘ 0.5^\circ per minute, so it travelled

[ 3 ( 60 ) + 40 ] ( 0.5 ) = 11 0 ∘ [3(60)+40](0.5) = 110^\circ

With reference to 12 12 , the minute hand travels 6 ∘ 6^\circ per minute, so it travelled

40 ( 6 ) = 24 0 ∘ 40(6)=240^\circ

Therefore, the smaller angle formed is 240 − 110 = 13 0 ∘ 240-110=\boxed{130^\circ}

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