Question

The sides BA and DC of a quadrilateral
are produced as shown in the given figure.
Prove that x+y = a + b.
​

Answer 1

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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

HENCE PROVED