What is the measure of the obtuse angle formed by the hour and minutes hands of a clock at 1: 26?

113°

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 26 min, the minute hand will travel

θm = 26 × 6

     = 156°

Calculate the angle of the hour hand (θh)

The hour hand travels 360° in 12 h, so it travels 30°  in 1 h

It has travelled for 1 h 26 min = 1²⁶/₆₀ h.

θh = 1²⁶/₆₀ × 30

    = 86/60 × 30

    = 43°

Calculate the angle between the hands

θ =  θm - θh

  = 156 - 43

  = 113°

The angle between the hands is 113°.

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