To calculate the angles for a pie chart, you can use the following formula:

When creating a pie chart, each slice visually represents the proportion of a specific category relative to the total. To determine the angle for each slice, you first need to calculate the fraction of the total that each category accounts for. This is achieved by dividing the category value by the total value of all categories combined. After obtaining this fraction, you multiply it by $360$ degrees, as a complete circle encompasses $360$ degrees.

For instance, consider a category that represents a value of $25$ out of a total of $100$. The angle for this category can be calculated as follows:

This indicates that the slice corresponding to this category will occupy $90$ degrees of the pie chart.

This calculation method ensures that all slices together form a complete circle, accurately reflecting the proportions of each category. It provides a clear and straightforward way to visualize data, allowing for quick comparisons between different categories.

Always remember to double-check your calculations to confirm that the sum of all angles equals $360$ degrees, which verifies the accuracy of your pie chart.