Question

Question 4
In the given figure, if $x+y=w+z,$ then prove that AOB is a line.

Answer 1

It can be observed that,
$x+y+z+z={360}^{\circ }$ ( 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, AOB is a line.