In the given figure, if $x+y=w+z$, then prove that $\mathrm{AOB}$ is a line.


It can be observed that,

$x+y+z+w=360^{\circ}$ (Complete angle)

It is given that,


$\therefore x+y+x+y=360^{\circ}$



Since $x$ and $y$ form a linear pair, $A O B$ is a line.

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