Angles of Polygon
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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