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# In figure, if x + y = w + z, then prove that AOB is a line.

Since, x,y,w and z are angles at a single point,
x + y + w + z = $$360^\circ$$

But it is given that, x + y = w + z

$$\because$$ x + y + x + y = $$360^\circ$$
$$\Rightarrow$$ 2(x + y) = $$360^\circ$$
$$\Rightarrow$$ (x + y) = $$180^\circ$$

Hence, by converse of linear pair axiom, it is proved that AOB is a straight line.