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Angles of Polygon

Sep 10, 2022
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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. 

Triangle 

Types of triangles 

Based on sides 

Based on sides 

Based of angles 

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°

Angle sum property of a triangle 

Quadrilateral 

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

Quadrilateral

The sum of angles of a quadrilateral is 360°.

Pentagon 

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

parallel
Pentagon 

The sum of angles of a pentagon is 540°. 

Hexagon 

A 6-sided polygon is called a hexagon. 

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. 

interior angles of a 𝒏-sided polygon 

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

parallel

Regular polygon 

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

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

exterior angle of a polygon. 

Sum of exterior angles of a polygon 

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

exterior angles of a polygon

Exercise

  • What is the value of x ?
Exercise 1
  • What are the measures of the exterior angles of the polygon shown?
Exercise 2
  • 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?
Exercise 4
  • Find the value of x and the measure of each interior angle.
Exercise 5

Concept Map

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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