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Question

Sides AB and CD of a quadrilateral ABCD are produced as shown in the following figure. Show that x+y=a+b.

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Solution

In quadrilateral ABCD
CDA=180-yABC=180-x
Since, the sum of the angles of a quadrilateral is 180, therefore
CDA+DAB+ABC+BCD=360180-y+a+180-x+b=360a+b=x+y
Hence, a+b=x+y.

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