It is given in the question that:

x + y = w + z

To prove,

AOB is a line or x + y = 180^o (Linear pair)

Now, according to the question,

x + y + w + z = 360^o (Angles at a point)

(x + y) + (w + z) = 360^o

(x + y) + (x + y) = 360^o (Given, x + y = w + z)

2 (x + y) = 360^o

(x + y) = 180^o

Therefore, x + y makes a linear pair.

And, AOB is a straight line