To calculate the angle between the hour and minute hands of a clock at 7:46, we can break the process down into steps:

Step 1: Calculate the position of the minute hand

The minute hand moves 360° in 60 minutes, so it moves $6^\circ$ per minute.

At 46 minutes: $\text{Angle of the minute hand} = 46 \times 6 = 276^\circ$ This means the minute hand is 276° from the 12 o'clock position.

Step 2: Calculate the position of the hour hand

The hour hand moves 30° per hour (since $360^\circ \div 12 = 30^\circ$). At exactly 7:00, the hour hand is at: $\text{7 o'clock position} = 7 \times 30 = 210^\circ$ However, since it's 46 minutes past 7, the hour hand has moved further. The hour hand moves $0.5^\circ$ per minute (since $30^\circ \div 60 = 0.5^\circ$).

So, in 46 minutes, the hour hand moves: $46 \times 0.5 = 23^\circ$ Thus, the total position of the hour hand is: $\text{Angle of the hour hand} = 210^\circ + 23^\circ = 233^\circ$

Step 3: Calculate the angle between the hour and minute hands

The angle between the hands is the absolute difference between their positions: $\text{Angle between the hands} = |276^\circ - 233^\circ| = 43^\circ$

Therefore, the degree of the hands of the clock at 7:46 is 43 degrees.

Would you like more details on this, or have any questions?

Here are 5 related questions to expand on this topic:

1. How do you calculate the angle between the hands of a clock at 3:15?
2. What is the smallest angle between the hands of the clock at 9:20?
3. How many degrees does the hour hand move in 10 minutes?
4. How can you calculate the angle of the hands at any given time?
5. How does the speed of the hour hand compare to that of the minute hand?

Tip: When calculating clock angles, always remember that the minute hand moves 6° per minute, while the hour hand moves 0.5° per minute.