Solution:
It can be observed that,
$x+y+z+w=360^{\circ}$ (Complete angle)
It is given that,
$x+y=z+w$
$\therefore x+y+x+y=360^{\circ}$
$2(x+y)=360^{\circ}$
$x+y=180^{\circ}$
Since $x$ and $y$ form a linear pair, $A O B$ is a line.
Solution:
It can be observed that,
$x+y+z+w=360^{\circ}$ (Complete angle)
It is given that,
$x+y=z+w$
$\therefore x+y+x+y=360^{\circ}$
$2(x+y)=360^{\circ}$
$x+y=180^{\circ}$
Since $x$ and $y$ form a linear pair, $A O B$ is a line.