What will be the measurement of the angle made by the hands of a clock when the time is 8:40?

The minute hand completes a full circle (360°) in 60 minutes, moving 6° per minute.

The hour hand completes a full circle (360°) in 12 hours (720 minutes), moving 0.5° per minute. Each hour gap is 30° (360° ÷ 12), and the hour hand takes 60 minutes to cover it.

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At 8:40, the minute hand is at 40 minutes.

Position from 12 o'clock:

$40 \times 6° = 240°$

The minute hand is pointing at "8" on the clock.

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At exactly 8:00, the hour hand would be at:

$8 \times 30° = 240°$

However, 40 minutes have passed, so the hour hand has moved ahead:

$40 \times 0.5° = 20°$

Hour hand position:

$240° + 20° = 260°$

The hour hand is between 8 and 9, closer to 9.

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Angle between the hands:

$|260° - 240°| = 20°$

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Using the formula $|30H - \frac{11M}{2}|$ where $H$ = hours and $M$ = minutes:

$|30(8) - \frac{11(40)}{2}|$

$= |240 - 220|$

$= 20°$

Therefore, the angle between the hands at 8:40 is $20°$ (Option 1).