Question

The sides BA and DC of a quadrilateral ABCD are produced as shown in the figure. Prove that a+b= x+y, if AB || DC. [CCE 2011 D С у a b A B​​

Answer 1

a+b=x+y

In quadrilateral ABCD,

∠A=180−b

and ∠C=180−a

Sum of all the angles of a quadrilateral is:

∠A+∠B+∠C+∠D=360

o

⇒180−b+x+180−a+y=360

⇒360−a−b+x+y=360

⇒a+b=x+y

Answer 2

Answer:

In quadrilateral ABCD,

∠A=180−b

and ∠C=180−a

Sum of all the angles of a quadrilateral is:

∠A+∠B+∠C+∠D=360°

⇒180−b+x+180−a+y=360

⇒360−a−b+x+y=360

⇒a+b=x+y