How can you determine the measure of an interior angle in a regular polygon?

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To find the measure of an interior angle of a regular polygon, you can follow a simple formula. A regular polygon is a shape with all sides and angles equal. Here’s how you can calculate the angle:

  1. Identify the number of sides (n): Determine how many sides your regular polygon has. This is crucial because the number of sides directly affects the angle measurement.
  2. Use the formula: The formula to find the measure of an interior angle of a regular polygon is:

    3. Interior Angle = ((n – 2) × 180) / n

  3. Calculate: Plug in the number of sides (n) into the formula. For example, if you have a hexagon (which has 6 sides):
    • n = 6
    • Interior Angle = ((6 – 2) × 180) / 6
    • Interior Angle = (4 × 180) / 6
    • Interior Angle = 720 / 6
    • Interior Angle = 120 degrees
  4. Conclusion: Thus, each interior angle of a regular hexagon is 120 degrees. Use this method to calculate the angle for any regular polygon by substituting the number of sides into the formula.

This approach not only gives you the angle measurement but also helps you understand the relationship between the number of sides and the interior angle in polygons!

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