Angle sum property of Quadrilateral at Algebra Den

Arithmetic

Additive Identity
Arithmetic Progression
Associative Property
Averages
Brackets
Closure Property
Commutative Property
Conversion of Measurement Units
Cube Root
Decimal
Distributivity of Multiplication over Addition
Divisibility Principles
Equality
Exponents
Factors
Fractions
Fundamental Operations
H.C.F / G.C.D
Integers
L.C.M
Multiples
Multiplicative Identity
Multiplicative Inverse
Numbers
Percentages
Profit and Loss
Ratio and Proportion
Simple Interest
Square Root
Unitary Method

Algebra

Cartesian System
Order Relation
Polynomials
Probability
Standard Identities & their applications
Transpose

Geometry

Basic Geometrical Terms
Circle
Curves
Angles
Define Line, Line Segment and Rays
Non-Collinear Points
Parallelogram
Rectangle
Rhombus
Square
Three dimensional object
Trapezium
Triangle
Quadrilateral

Trigonometry

Trigonometry Ratios

Data-Handling

Arithmetic Mean
Frequency Distribution Table
Graphs
Median
Mode
Range

Videos
Solved Problems

Home >> Quadrilateral >> Angle sum property of Quadrilateral >>

Angle sum property of Quadrilateral

Angle sum property of Quadrilateral Construction of Quadrilateral (compass)

Before you understand the angle sum property of a quadrilateral, you are advised to read:

What is Quadrilateral ?
What is Triangle ?
What is Angle Sum Property of Triangle ?

Angle Sum property of a quadrilateral says that sum of all angles of a quadrilateral is equal to 360 degree

Now, observe the following diagram:

Angle Sum property of a quadrilateral we get:
∠ A + ∠ B + ∠ C + ∠ D = 360°

Now, let's prove angle sum property of a quadrilateral:

Observe the following diagram:

Above diagram represent: Quadrilateral ABCD
BD is a diagonal which divides the given quadrilateral into two triangles i.e. △ ABD and △ BCD

In △ ABD:
∠ A + ∠ ABD + ∠ BDA = 180° ..... (Angle Sum property of triangle)

Similarly, In △ BCD:
∠ C + ∠ CDB + ∠ CBD = 180°

Now, add the values of △ ABD and△ BCD & we get:
∠ A + ∠ ABD + ∠ BDA + ∠ C + ∠ CDB + ∠ CBD = 180° + 180°

Or we can write it as:
∠ A + ∠ ABD + ∠ CBD + ∠ BDA + ∠ CDB + ∠ C = 180° + 180°

Now, ∠ ABD + ∠ CBD = ∠ B and ∠ BDA + ∠ CDB = ∠ D & we get:
∠ A + ∠ B + ∠ C + ∠ D = 360°

Hence proved, angle sum property of a quadrilateral.