Question

Find the angle traced by hour hand of a correct clock between 7 pm 0' clock and 2 am 0' clock.

• A. \( 200^\circ \)
• B. \( 210^\circ \)
• C. \( 310^\circ \)
• D. \( 290^\circ \)

Hint:

\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.

Answer 1

The Correct Option is B

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 \( 210^\circ \).