At half past 8 the minute hand points towards 6 and the hour hand points towards 2(1/2) marks between 8 and 9. The angle between 6 and 8 is 60 degree and the angle 2(1/2) min. space is 15 degree. hence, total angle between two hands is 75 degree.

Angle of the Hands of a Clock at Half Past 8

To determine the angle at which the hands of a clock are inclined when it is half past 8, we need to consider the positions of the hour and minute hands separately.

Position of the Hour Hand:
At half past 8, the hour hand will be pointing between the 8 and 9 on the clock face. To calculate the exact position, we need to consider that the hour hand moves 30 degrees per hour, or 0.5 degrees per minute.

At 8 o'clock, the hour hand is at the 8 marker, which is 240 degrees from the 12 marker on the clock face. Since half an hour has passed, the hour hand will have moved an additional 0.5 degrees per minute multiplied by 30 minutes, which equals 15 degrees.

Therefore, the position of the hour hand at half past 8 is at 240 degrees + 15 degrees = 255 degrees.

Position of the Minute Hand:
At half past 8, the minute hand will be pointing at the 6 marker on the clock face since half an hour is equivalent to 30 minutes.

The minute hand moves 360 degrees in 60 minutes, so for 30 minutes, it will move half of that distance. Hence, the minute hand will be at 180 degrees.

Angle between the Hour and Minute Hands:
To find the angle between the hour and minute hands, we subtract the position of the hour hand from the position of the minute hand.

Angle = Position of Minute Hand - Position of Hour Hand
Angle = 180 degrees - 255 degrees
Angle = -75 degrees

Since the angle is negative, we consider the absolute value, which is 75 degrees.

Therefore, the angle between the hour and minute hands at half past 8 is 75 degrees.

Conclusion:
The angle at which the hands of a clock are inclined when it is half past 8 is 75 degrees.