A clock is started at noon. By 20 minutes past 5 PM on the same day, the angle through which the hour hand has turned is

Options

A. `150^(@)`
B. `160^(@)`
C. `145^(@)`
D. `155^(@)`

Explanation

To find the angle through which the hour hand of a clock has turned from noon to 20 minutes past 5 PM, we can follow these steps:

### Step 1: Determine the total time from noon to 20 minutes past 5 PM.
- From noon (12:00 PM) to 5:00 PM is 5 hours.
- Then, add the additional 20 minutes.
- Total time = 5 hours + 20 minutes = 5 hours + (20/60) hours = 5 + 1/3 hours = 16/3 hours.

### Step 2: Calculate the angle turned by the hour hand.
- The hour hand completes a full rotation (360 degrees) in 12 hours.
- Therefore, the angle turned by the hour hand in 1 hour = 360 degrees / 12 hours = 30 degrees per hour.

### Step 3: Calculate the total angle turned in 16/3 hours.
- Total angle = (Angle per hour) × (Total hours)
- Total angle = 30 degrees/hour × (16/3 hours) = 30 × 16/3 = 160 degrees.

### Conclusion:
The angle through which the hour hand has turned from noon to 20 minutes past 5 PM is **160 degrees**.

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