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.