Can You Determine Right Time? Trivia Quiz

Explanation
At 4:08, the hour hand will be slightly past the 4 mark, while the minute hand will be at the 8 mark. To calculate the angle between the hands, we can use the formula: angle = |30H - 11/2M|, where H is the hour and M is the minute. Plugging in the values, we get: angle = |30(4) - 11/2(8)| = |120 - 44| = |76| = 76 degrees. Therefore, the correct answer is 76 degrees.

Explanation
At 3:00 PM, the hour hand points at the 3 on the clock while the minute hand points at the 12. From 3:00 PM to 3:45 PM, the hour hand moves slightly past the 3, while the minute hand moves 3/4 of the way around the clock. The angle between the hour and minute hand can be calculated by finding the difference between the angles they make with the 12 on the clock. Since the minute hand moves 3/4 of the way around the clock, it covers an angle of 270 degrees. The hour hand moves slightly past the 3, which is approximately 1/4 of the way between the 3 and 4 on the clock. This corresponds to an angle of 30 degrees. Therefore, the angle between the hour and minute hand is 270 degrees - 30 degrees = 240 degrees. However, since the question asks for the angle between the hands, we subtract this angle from 360 degrees to find that the angle is 360 degrees - 240 degrees = 120 degrees. Therefore, the correct answer is 120 degrees.

Explanation
At 4:32, the hour hand is pointing between the 4 and 5, while the minute hand is pointing at the 32-minute mark. To find the angle between the hands, we need to calculate the angle formed by the hour hand and the 12 o'clock position, as well as the angle formed by the minute hand and the 12 o'clock position. The hour hand moves 360 degrees in 12 hours, so in 32 minutes it moves (32/60) * (360/12) = 160 degrees. The minute hand moves 360 degrees in 60 minutes, so in 32 minutes it moves (32/60) * 360 = 192 degrees. The difference between these two angles is 192 - 160 = 32 degrees. Since the angle between the hands is always the smaller angle, the answer is 32 degrees.

Explanation
The hands of a clock are at right angles to each other when the minute hand is at the 3, 6, 9, or 12 position and the hour hand is in between two hour marks. In this case, the minute hand is at the 2 position at 11:10 and at the 9 position at 11:43, making the hour and minute hands at right angles to each other.

Explanation
At 5:24, the hour hand is between the 5 and 6 on the clock face. Since there are 12 hours on a clock, each hour represents 30 degrees (360 degrees divided by 12). The hour hand is 24 minutes past the 5, which is 24/60 of an hour. Therefore, the hour hand has moved an additional 24/60 * 30 degrees, which is 12 degrees. Adding this to the angle of the hour hand at 5 o'clock (150 degrees), we get a total angle of 162 degrees.