Question

The sides BA and DC of a quadrilateral

ABCD are produced as shown in the figure.

Prove that a + b = x + y ​

Answer 1

Answer:

In quadrilateral ABCD,

In quadrilateral ABCD, ∠A=180−b

In quadrilateral ABCD, ∠A=180−band ∠C=180−a

In quadrilateral ABCD, ∠A=180−band ∠C=180−aSum of all the angles of a quadrilateral is:

In quadrilateral ABCD, ∠A=180−band ∠C=180−aSum of all the angles of a quadrilateral is:∠A+∠B+∠C+∠D=360

In quadrilateral ABCD, ∠A=180−band ∠C=180−aSum of all the angles of a quadrilateral is:∠A+∠B+∠C+∠D=360 o

In quadrilateral ABCD, ∠A=180−band ∠C=180−aSum of all the angles of a quadrilateral is:∠A+∠B+∠C+∠D=360 o

In quadrilateral ABCD, ∠A=180−band ∠C=180−aSum of all the angles of a quadrilateral is:∠A+∠B+∠C+∠D=360 o ⇒180−b+x+180−a+y=360

In quadrilateral ABCD, ∠A=180−band ∠C=180−aSum 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

In quadrilateral ABCD, ∠A=180−band ∠C=180−aSum 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

Hence proved

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