The angle between the hour and minute hands of a clock at 5:10 can be calculated using the following approach:

### Step 1: Calculate the position of the hour hand
Each hour on the clock represents an angle of 30 degrees (since \( 360^\circ / 12 = 30^\circ \) per hour). At exactly 5:00, the hour hand is at:
\[
5 \times 30^\circ = 150^\circ
\]

However, at 5:10, the hour hand has moved slightly ahead because it's not exactly at 5:00. The hour hand moves 0.5 degrees per minute (since \( 30^\circ / 60 = 0.5^\circ \) per minute). So in 10 minutes, the hour hand moves:
\[
10 \times 0.5^\circ = 5^\circ
\]
Thus, the position of the hour hand at 5:10 is:
\[
150^\circ + 5^\circ = 155^\circ
\]

### Step 2: Calculate the position of the minute hand
Each minute represents an angle of 6 degrees (since \( 360^\circ / 60 = 6^\circ \)). At 10 minutes, the minute hand is at:
\[
10 \times 6^\circ = 60^\circ
\]

### Step 3: Calculate the angle between the two hands
The angle between the hour and minute hands is the absolute difference between their positions:
\[
| 155^\circ - 60^\circ | = 95^\circ
\]

So, the angle at 5:10 is **95 degrees**.

Would you like more details or have any questions about the calculation?

Here are 5 related questions for further exploration:
1. What is the angle between the hands at 7:25?
2. How do you calculate the angle between the hands at any given time?
3. What is the reflex angle at 5:10?
4. How would the angle change at 5:20?
5. What is the smallest angle between the hands at 4:45?

**Tip:** The minute hand moves 6 degrees per minute, while the hour hand moves 0.5 degrees per minute.

Discover how to calculate the angle between the hour and minute hands of a clock at 5:10. This step-by-step guide explains the core geometry principles and formulas involved, making it perfect for students in Grades 6-8. The solution shows that the angle is 95 degrees.

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