Find the angle traced by hour hand of a correct clock between 7 pm 0' clock and 2 am 0' clock.
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\textbf{Angle Traced by Clock Hands.} Remember that the hour hand moves \( 360^\circ \) in 12 hours (or \( 30^\circ \) per hour), and the minute hand moves \( 360^\circ \) in 60 minutes (or \( 6^\circ \) per minute). To find the angle traced over a specific time interval, calculate the number of hours (for the hour hand) or minutes (for the minute hand) and multiply by the respective degrees per unit time.
The time interval is from 7 pm to 2 am.
From 7 pm to 12 am (midnight), the number of hours is \( 12 - 7 = 5 \) hours.
From 12 am to 2 am, the number of hours is 2 hours.
The total number of hours between 7 pm and 2 am is \( 5 + 2 = 7 \) hours.
In a 12-hour clock, the hour hand moves \( 360^\circ \) in 12 hours.
Therefore, the angle moved by the hour hand in one hour is \( \frac{360^\circ}{12} = 30^\circ \).
The total angle traced by the hour hand in 7 hours is \( 7 \times 30^\circ = 210^\circ \).
Thus, the angle traced by the hour hand of a correct clock between 7 pm 0' clock and 2 am 0' clock is \( 210^\circ \).