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

### 2. Quadrilateral:

- 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:

- Regular Polygon: A polygon is said to be regular when all its sides and interior angles are equal.
- Irregular polygons: A polygon is said to be irregular when all its sides and interior angles are of different measures.
- 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.
- 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:

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

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