a polygon with 9 sides

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nonogon

A polygon with 9 sides is called a nonagon. To understand how to determine the various properties of a nonagon, let's break it down step by step:

1. Side length: If you have a nonagon where the side lengths are equal, you can find the length of each side by measuring the distance between any two adjacent vertices.

2. Perimeter: The perimeter of a nonagon is the sum of all its side lengths. So, to find the perimeter, you would need to add up the lengths of all nine sides.

3. Interior angles: To calculate the measure of each interior angle of a regular nonagon (where all angles are equal), you can use the formula: ((n-2) * 180) / n, where n is the number of sides. Substituting n = 9, you get ((9-2) * 180) / 9 = 140 degrees.

4. Sum of interior angles: The sum of all interior angles of any polygon can be calculated using the formula: (n-2) * 180, where n is the number of sides. Substituting n = 9, you get (9-2) * 180 = 1260 degrees.

5. Exterior angles: The measure of an exterior angle of a regular polygon can be obtained by dividing 360 degrees by the number of sides. So, for a nonagon, each exterior angle would be 360 / 9 = 40 degrees.

Remember, these formulas are applicable to regular nonagons. If the nonagon in question is irregular (having sides and/or angles that are not equal), you would need additional information to calculate its properties.