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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.


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