Nonagon

A nonagon is a polygon that has nine sides and nine angles. It is also known as a 9-gon. The sum of the interior angles in a nonagon can be found using the formula:

Sum of interior angles = (n - 2) * 180°

Where n is the number of sides in the nonagon. In the case of a nonagon:

Sum of interior angles = (9 - 2) * 180° = 7 * 180° = 1260°

Each interior angle in a regular nonagon measures:

Each interior angle = Sum of interior angles / Number of sides

Each interior angle = 1260° / 9 = 140°

Therefore, each interior angle in a regular nonagon measures 140°.

Properties of a Nonagon

Here are some key properties of a nonagon:

1. A nonagon has 9 sides and 9 angles.
2. The sum of the interior angles of a nonagon is 1260°.
3. Each interior angle in a regular nonagon measures 140°.
4. A nonagon can be regular or irregular.
5. The area of a nonagon can be calculated using various methods, such as dividing the nonagon into smaller shapes and finding their areas.
6. The perimeter of a nonagon can be found by adding the lengths of its 9 sides.

Sample Problems

1. Find the sum of the interior angles of a nonagon.

Answer:

The sum of the interior angles of a nonagon is 1260°.

2. What is the measure of each interior angle in a regular nonagon?

Answer:

Each interior angle in a regular nonagon measures 140°.

Conclusion

Understanding the properties and formulas related to a nonagon is important in geometry. Practicing problems related to nonagons can help in mastering the concepts.