What will be the measurement of the angle made by the hands of a clock when the time is 6:14?

The minute hand moves $360°$ in $60$ minutes, so it moves $6°$ per minute.

At $14$ minutes, the minute hand is at:

$14 \times 6° = 84°$ from 12 o'clock

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The hour hand moves $360°$ in $12$ hours $(720$ minutes$)$, so it moves $0.5°$ per minute.

At $6:14$:

• At $6:00$, the hour hand is at $180°$ from 12 o'clock
• In the additional $14$ minutes, it moves $14 \times 0.5° = 7°$

Position of hour hand:

$180° + 7° = 187°$ from 12 o'clock

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The angle between the two hands:

$|187° - 84°| = 103°$

Therefore, the angle made by the hands at $6:14$ is $103°$.