Final answer:
The angle between the minute hand and the hour hand of a clock at 8:30 is calculated by finding the positions of each hand and then determining their angle difference. At 8:30, the minute hand is at 180°, while the hour hand is at 255°, resulting in an angle of 75° between them. Thus, the correct answer is c. 75.
Step-by-step explanation:
To find the angle between the minute hand and the hour hand of a clock when the time is 8:30, we need to perform a step-by-step calculation using the positions of the hands. At 8:30, the minute hand is at the 6, indicating 30 minutes past the hour, while the hour hand is halfway between the 8 and the 9, indicating halfway through the eighth hour.
Each hour on the clock represents an angle of 30° (since 360°/12 hours = 30° per hour). Half an hour would be half of 30°, which is 15°. Therefore, the hour hand is 8 * 30° + 15° = 255° from the top of the clock. The minute hand at 30 minutes is at the 6, which is 180° from the top of the clock.
The angle difference between the hour hand and the minute hand can be found by subtracting the smaller angle from the larger angle: 255° - 180° = 75°.
The correct answer to the question about the angle between the minute hand and the hour hand of a clock at 8:30 is c. 75.