# In Fig. 6.16, if x + y = w + z, then prove that AOB is a line. Given: x + y = w + z

To prove,: AOB is a line or x + y = 180° (Linear pair)

Proof:

Now, according to the question,

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

(x + y) + (w + z) = 360°

(Given, x + y = w + z)

2 (x + y) = 360o

(x + y) = 180o

Therefore, x + y makes a linear pair.

And, AOB is a straight line

Hence, Proved.

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