Question

state and prove angle sum property of a quadrilateral

Answer 1

Angle Sum Property
Of Quadrilateral

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We can prove this property by drawing a diagonal of the quadrilateral.
this diagonal will divide quadrilateral into two triangles .
as we know sum of all angles of a triangle is 180*
then,

180* + 180* = 360*


hence, it is proved that all angles of a quadrilateral sum up to 360*

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Answer 2

In The given figure !

∠D + ∠DAC + ∠DCA = 180 ( angle sum property of triangle ) ---(1)

Similarly 

∠B + ∠CAB + ∠ACB = 180 ---(2) 

Adding 1 and 2 

∠D + ∠B  + (∠DAC +  ∠CAB ) + (∠DCA + ∠ACB ) = 180 + 180 

∠D + ∠B+ ∠A + ∠C = 360 

Hence proved