Question

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

Answer 1

By complete angle property
X+y+w+z=360
x+y+x+y=360(given x+y=w+z)
2x+2y=360
2(x+y)=360
x+y=180
Hence AOB is a line

Answer 2

because angle x and angle y is a linear pair and also angle w and angle z is also linear pair.
so,
angleAYC+angleBXC=180 and
angle z+angle w = 180
these pairs are forming on a straight line AOB.
AOB is a line.
Hence proved.