What are the angles of the hands of the clock when the time is 1:35?

To find the angles of the hands of the clock at 1:35, we need to calculate both the angle made by the hour hand and the minute hand.

### 1. Minute hand angle:
Each minute on the clock represents 6 degrees because:
\[
\frac{360^\circ}{60 \text{ minutes}} = 6^\circ/\text{minute}
\]
At 35 minutes, the angle of the minute hand is:
\[
35 \times 6 = 210^\circ
\]
So, the minute hand is at \(210^\circ\).

### 2. Hour hand angle:
Each hour on the clock represents 30 degrees because:
\[
\frac{360^\circ}{12 \text{ hours}} = 30^\circ/\text{hour}
\]
At 1:00, the hour hand would be at \(30^\circ\), but at 1:35, the hour hand has moved slightly. It moves 0.5 degrees per minute because:
\[
\frac{30^\circ}{60 \text{ minutes}} = 0.5^\circ/\text{minute}
\]
In 35 minutes, the hour hand moves:
\[
35 \times 0.5 = 17.5^\circ
\]
Thus, the hour hand at 1:35 is:
\[
30^\circ + 17.5^\circ = 47.5^\circ
\]

### Conclusion:
- The minute hand is at \(210^\circ\).
- The hour hand is at \(47.5^\circ\).

Would you like further details or explanations?

Here are five related questions to consider:
1. What is the angle between the hour and minute hands at 1:35?
2. How do you calculate the angle between clock hands at any given time?
3. What time between 1:00 and 2:00 do the hour and minute hands overlap?
4. How would the angles change at 2:35 instead of 1:35?
5. How can this method be used to find the time when the hands form a specific angle?

**Tip:** To calculate angles quickly, remember that the hour hand moves 0.5 degrees per minute, while the minute hand moves 6 degrees per minute.

Discover how to calculate the angles of the hour and minute hands on a clock at 1:35. This problem involves geometry and time, with the minute hand at 210 degrees and the hour hand at 47.5 degrees. Perfect for students in Grades 5-7 learning about clock angles.

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