## Key Concepts

- Define a quadrilateral.
- Find the sum of angles of a quadrilateral.
- Find the sum of interior angles of an n-sided polygon.
- Guess the measure of each angle of a regular polygon.
- Find the sum of exterior angles of n-sided polygon.

## Triangle

A triangle is a polygon with three edges and three vertices.

### Types of triangles

#### Based on sides

#### Based of angles

### Angle sum property of a triangle

Angle sum property of a triangle states that the sum of angles of a triangle is180°

### Quadrilateral

In geometry, a four-sided polygon, having four edges (sides) and four corners (vertices), is a **quadrilateral**.

The sum of angles of a quadrilateral is 360°.

### Pentagon

A figure that has five sides and five vertices is called a **pentagon.**

The sum of angles of a pentagon is 540°**.**

### Hexagon

A 6-sided polygon is called a **hexagon.**

The sum of angles of a hexagon is 720°

### Sum of interior angles of a 𝒏-sided polygon

There are n−2 triangles in each n sided polygon.

The sum of the measures of the interior angles of a convex 𝒏 -gon is 𝟏𝟖𝟎°×𝒏−𝟐.

### Regular polygon

A polygon that is equilateral (all sides have the same length) and whose angles are of equal measures is a **regular polygon**.

The measure of interior angles of a regular 𝒏 -gon is 180°×(n−2)/n

### Exterior angle of a polygon

The angle between any side of a polygon and a line extended from the next side is called an **exterior angle of a polygon**.

### Sum of exterior angles of a polygon

The sum of all the exterior angles of a polygon is 360°.

## Exercise

- What is the value of x ?

- What are the measures of the exterior angles of the polygon shown?

- The sum of the interior angles of a regular n-gon is 6, . What is the measure of each interior angle?
- What is the value of x? What is the measure of each exterior angle?

- Find the value of x and the measure of each interior angle.

### Concept Map

### What we have learned

- In geometry, a four-sided polygon, having four edges (sides) and four corners (vertices) is a quadrilateral.
- The sum of the measures of the interior angles of a convex 𝒏-gon is 180° ( n-2 )
- A polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length) is a regular polygon.
- The measure of interior angles of a regular 𝒏-gon is 180° x (n-2)/n
- The angle between any side of a polygon and a line extended from the next side is called an exterior angle of a polygon.
- The sum of all the exterior angles of a polygon is 360°

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