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To find the central angle that represents the number of families with monthly incomes between $1000 and $2000, we can use the formula for calculating the central angle in a pie chart:

\[
\text{Central Angle} = \left(\frac{\text{Number of Families in Category}}{\text{Total Number of Families}}\right) \times 360^\circ
\]

### Given Data:
- Number of families with incomes between $1000 and $2000: 44
- Total number of families surveyed: 90

Now, let's calculate the central angle:

\[
\text{Central Angle} = \left(\frac{44}{90}\right) \times 360^\circ
\] 

Let me calculate that.The central angle that represents the number of families with monthly incomes between $1000 and $2000 is $ 176^\circ $.

Let me know if you would like further details or explanations.

Here are 5 related questions:
1. How do we calculate the central angle for the other income categories?
2. What is the total percentage of families with incomes below $1000?
3. How would the central angle change if the number of families with incomes between $1000 and $2000 increased?
4. What is the significance of the total central angle summing up to 360 degrees?
5. How could this data be visualized using a bar chart instead of a pie chart?

**Tip**: When visualizing data using a pie chart, each sector's angle is proportional to the corresponding data category's percentage of the total.

What will be the central angle of the sector that represents the number of families with monthly incomes between $1000 and $2000?

Learn how to calculate the central angle for families with monthly incomes between $1000 and $2000 based on a survey of 90 families. This example covers pie chart construction and percentage-based angle calculation. Suitable for middle school students.

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