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°
Related topics
Square 1 to 20 : Chart, Table, Perfect Squares and Examples
Square 1 to 20 When you multiply a number by itself, the result is called a square. And when you’re preparing for exams, you need to have a foundation for algebra and quick mental math because you get a really short time to do your exam. Therefore, learning the squares from one to twenty is […]
Square 1 to 40 : Table, Perfect Squares, Chart and Examples
Square 1 to 40 When you multiply a number by itself, the resulting number is a square, and if you are someone who is either appearing in a competitive exam or just wants to do well in math in school, knowing square 1 to 40 is a really important skill. But manually multiplying every time, […]
Square Root : Definition, Formula, Methods and Types Explained
Square Root Square roots are one of those seemingly daunting maths topics that appear in many different situations, from algebra to geometry. Yet the concepts behind them aren’t as hard to grasp. It makes handling numbers far easier if you know the concept well. Let us understand how to find the square roots of a number […]
Cubes 1 to 20 : Chart, Table, Memory Tricks and Examples
Most students don’t struggle much with smaller cubes like 2³ or 3³. Those usually come quickly. The hesitation starts with numbers like 11³ or 17³. Or when someone suddenly asks, what is 20 cubed? That pause is not a memory problem. It’s about the lack of proper understanding and hence confidence. Naturally, learning cubes 1 […]
Other topics
Comments: