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

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

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Assume AOB is a line.

Therefore, x + y = 180° …(1)

[Linear pair axiom]

w + z = 180° …(2)

[Linear pair axiom]

Now, from (1) and (2)

x + y = w + z