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    Minute hand was runned 30'

    => Location of minute hand at number 6 and equal 1/2 circle

    Now location of hour hand at number 3 plus 1/2 distance from number 3 to number 4

    => Location of hour hand equal 112⋅3+12⋅112=724(circle)112⋅3+12⋅112=724(circle)

    So the difference of minute hand and hour hand is: 12−724=524(circle−of−clock)12−724=524(circle−of−clock)

    A circle of clock = 360o 

    => 524−circle−of−clock=360o⋅524=75o524−circle−of−clock=360o⋅524=75o

    So the measure of the smaller angle formed by the minute hand and the hour hand of a clock at 3:30 is 75o

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