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The side BA and DC of a quadrilateral AB...

The side BA and DC of a quadrilateral ABCD are produced to E and F respectively. If `angleBCF=a^(0),angleABC=x^(@), angleADC=y^(@)and angleDAE=b^(@),`
`"prove that"x+y=a+b.`

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`{:("We have",angle1+b^(@)=180^(@),),(implies,angle1=(180^(@)-b^(@)),("linear pair")),(Also,angle2+a^(@)=180^(@),("linear pair")),(implies,angleA+angleB+angleC+angleD = 360^(@),("sum of all the angles of a quadrilateral")),(implies,(180-b)^(@)+x^(@)+(180-a)^(@)+y^(@)=360^(@),),(implies,x+y=a+b,):}`
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