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# What Are The Properties Of Polygons?

In geometry, polygons are defined as a flat shape or two-dimensional figure enclosed by three or more straight lines. A polygon consists of two words poly that means ‘many’ and gon that means ‘angle”. Here in this article, we will learn about the properties of polygons.

## Different types of polygons and their properties:

### 1. Triangle:

•  It is formed by three line segments and has three vertices.
• It has no diagonals.
• The sum of all interior angles is 180 • It is formed by four line segments and has four vertices.
• It has two diagonals.
• The sum of all interior angles is 360 .

### 3. Pentagon:

• It is formed by five line segments and has five vertices.
• There are five diagonals in the pentagon.
• The sum of all interior angles is 540 ### 4. Hexagon:

• It is formed by six line segments and has six vertices.
• There are nine diagonals in a hexagon.
• The sum of all interior angles is 720 ### 5. Heptagon:

• It is formed by seven line segments and has seven vertices.
• There are fourteen diagonals.
• The sum of all interior angles is 900 ### 6. Octagon:

• It is formed by eight line segments and has eight vertices.
• There are twenty diagonals in this figure.
• The sum of all interior angles is 1000 ### 7. Nonagon:

• It is formed by nine line segments and has nine vertices.
• There are a total of twenty-seven diagonals.
• The sum of all interior angles is 1260 ### 8. Decagon:

• It is formed by ten line segments and has ten vertices.
• There are a total of thirty-five diagonals.
• The sum of all interior angles is 1440 ## Some other types of polygons:

1. Regular Polygon: A polygon is said to be regular when all its sides and interior angles are equal.
2. Irregular polygons: A polygon is said to be irregular when all its sides and interior angles are of different measures.
3. Convex Polygon: A polygon is said to be convex when the sum of all interior angles is less than 180 and vertex points outward from the center of a figure.
4. Concave Polygon: A polygon is said to be concave when one or more interior angles are more than 180 and vertex points inside of the figure.

## Basic properties of polygons based on their sides and angles:

1. The sum of all interior angles of a polygon having n-sides is (n-2)*180 2. The number of diagonals in a polygon having n sides is n(n-3)/2
3. The number of triangles that can be formed by joining diagonals from one corner of a polygon is n-2
4. The Interior angle of a regular polygon having n-sides can be measured by [(n-2)*180 ]/n
5. An exterior angle of a regular polygon having n-sides can be measured by 360 /n

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