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what is the smaller angle formed by the minute and hour hands at 3: 30pm?

75°

Step-by-step explanation:

Calculate the angle of the minute hand (θm)

The clock face is a circle of 360°, and there are 60 min in 1h,

So, the minute hand travels 6° in 1 min.

In 30 min, the minute hand will travel

θm = 30 × 6

     = 180°

Calculate the angle of the hour hand (θh)

The hour hand travels 360° in 12 h, so it travels 30° in 1 h and 0.5° in 1 min.

It has travelled for 3 h + 30 min

θh = (3 × 30) + (30 × 0.5)

    = 90 + 15

    = 105°

Calculate the angle between the hands

θ =  θm -  θh

  = 180 - 105

  = 75°

The angle between the hands is 75°.

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step-by-step explanation:

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step-by-step explanation:

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