Look at your watch face. Through how many right angles does the minute-hand moves between 8: 00 O’ clock and 10:30 O’ clock?

Options

A. 8
B. 12
C. 10
D. None of these

Answer

To solve the problem of how many right angles the minute hand moves between 8:00 and 10:30, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Movement of the Minute Hand**:
The minute hand completes a full circle (360 degrees) in 60 minutes.

**Hint**: Remember that a full circle is 360 degrees, and it takes 60 minutes for the minute hand to complete this.

2. **Calculate the Degrees per Minute**:
Since the minute hand moves 360 degrees in 60 minutes, we can find the degrees it moves per minute:
\[ \text{Degrees per minute} = \frac{360 \text{ degrees}}{60 \text{ minutes}} = 6 \text{ degrees per minute} \]

**Hint**: To find the degrees per minute, divide the total degrees by the total minutes.

3. **Determine the Total Time from 8:00 to 10:30**:
The time from 8:00 to 10:30 is 2 hours and 30 minutes. We can convert this into minutes:
\[ 2 \text{ hours} = 2 \times 60 = 120 \text{ minutes} \]
\[ 30 \text{ minutes} = 30 \text{ minutes} \]
Therefore, the total time is:
\[ 120 \text{ minutes} + 30 \text{ minutes} = 150 \text{ minutes} \]

**Hint**: Convert hours to minutes by multiplying the number of hours by 60 and then add any additional minutes.

4. **Calculate the Total Degrees Moved by the Minute Hand**:
Now, we can calculate the total degrees the minute hand moves in 150 minutes:
\[ \text{Total degrees} = 150 \text{ minutes} \times 6 \text{ degrees per minute} = 900 \text{ degrees} \]

**Hint**: Multiply the total minutes by the degrees the minute hand moves per minute to find the total degrees moved.

5. **Convert Degrees to Right Angles**:
Since 1 right angle is 90 degrees, we can find how many right angles are in 900 degrees:
\[ \text{Number of right angles} = \frac{900 \text{ degrees}}{90 \text{ degrees per right angle}} = 10 \text{ right angles} \]

**Hint**: To find the number of right angles, divide the total degrees by 90 degrees.

### Final Answer:
The minute hand moves through **10 right angles** between 8:00 and 10:30.