Question

Prove that the sum of angles of a quadrilateral is 360.


Please give answer fast.................its urgent.​

Answer 1

Given: A quadrilateral ABCD

To Prove: <A+<B+<C+<D= 360°

Construction: join BD

Proof: since the sum of the angles of a triangle is 180°, we have

<A+<1+<2= 180°......................(1) (sum of angles of triangle ABD)

and <3+<C+<4= 180..............(2) (sum of angles of triangle BCD)

On adding (1) and (2), we get

<A+<C+(<1+<3)+(<2+<4)=360

<A+<C+<B+<D= 360. ( since <1+<3=<B and <2+ <4=<A)

<A+<B+<C+<D = 360... proved....