Question

If A,B,C, and D are the angles of a Quadrilateral. Then, Prove that:

Answer 1

Hope this answers the question

Answer 2

In a quadrilateral ABCD, ∠A+∠B+∠C+∠D=360

(i)sin(A+B)+sin(C+D)=0

 sin(A+B)+sin(C+D)=2sin(2A+B+C+D).cos(2A+B−C−D)

=2sin(180).cos(2A+B−C−D)

=0

(ii)cos(A+B)=cos(C+D)

cos(A+B)−cos(C+D)= − 2 sin (2 A+B+C+D).sin(2A +B−C −D)0

cos(A+B)−cos(C+D)=0

cos(A+B)=cos(C+D)