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

Explanation

We have `angle A +b^(@) =180^(@) " " ` (linear pair)
`rArr angle a = (180^(@)-b^(@)). " " `...(i)
Also, `angle C+a^(@)=180^(@) " " `(linear pair)
`rArr angle C =(180^(@) -a^(@)). " " ` ...(ii)
Now, `angle A + angle B + angle C + angle D = 360^(@) ("sum of the "angle " of a quad. is "360^(@))`
`rArr (180^(@)-b^(@))+x^(@)+(180^(@)-a^(@))+y^(@)=360^(@) " " `[using (i) and (ii)]
`rArr x + y=a+b.`