Question

state the angle sum property of a quadrilateral​

Answer 1

Solution:-

Proof

Let ABCD be a quadrilateral join AC

Clearly ,   ∠1 +  ∠2 =  ∠A ........(i)

And  ∠3 +  ∠4 =  ∠C .........(ii)

We know that the sum of angle of triangle is 180⁰

Therefore , from ∆ABC , we have

 ∠2 +  ∠4 +  ∠B = 180⁰ ( angle sum property of triangle)

From ∆ACD we have

 ∠1 +  ∠3 +  ∠D = 180⁰ ( angle sum property of traingle)

Adding the angle on either side we get;

∠2 +  ∠4 +  ∠B + ∠1 +  ∠3 +  ∠D = 360⁰

(∠2 +   ∠1 +  ) + ∠B + (∠3 + ∠4 ) + ∠D = 360⁰

∠A + ∠B + ∠C + ∠D = 360⁰ using (i) and ( ii)

Hence sum of all four angle of quadrilateral is 360⁰

Note:- Figure is attached