Find the measure of each exterior angle of a regular polygon of 9 sides

General
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find the measure of each exterior angle of a regular polygon of 9 sides

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Find the measure of each exterior angle of a regular polygon of 9 sides

Answer:

To find the measure of each exterior angle of a regular polygon with n sides, you can use the formula for the exterior angle of a regular polygon:

\text{Exterior angle} = \frac{360^\circ}{n}

Here’s a step-by-step approach to find the measure of each exterior angle for a regular polygon with 9 sides (nonagon):

  1. Identify the number of sides (n):

    • For a regular nonagon, n = 9.

  2. Apply the formula:

    • Use the formula \text{Exterior angle} = \frac{360^\circ}{n}.

      \text{Exterior angle} = \frac{360^\circ}{9}

  3. Calculate the exterior angle:

    • Perform the division.

      \text{Exterior angle} = \frac{360^\circ}{9} = 40^\circ

So, the measure of each exterior angle of a regular polygon with 9 sides is 40^\circ.

Final Answer:
Each exterior angle of a regular polygon with 9 sides measures 40^\circ.