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

As Given, x+y=w+z
To Prove: AOB is a line or x+y=180° (linear pair)
According to the question, x+y+w+z=360° Angles around a point
(x+y)+(w+z)=360°
(x+y)+(x+y)=360° Given x+y=w+z
2(x+y)=360°
(x+y)=180°
Hence, x+y makes a linear pair.
Therefore, AOB is a straight line.