Question

In the figure x=z and y=w the prover that AOB is a straight line​

Answer 1

w+x+y+z=360(angles on same point)

x+x+y+y=360

2y+2x=360

2(x+y)=360

x+y=180

hence this angle are forming linear pair so lines are parallel.

Answer 2

Question :-

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

Answer :-

Sum of all the angles at a point = 360°

∴ x + y + z + w = 360° or, (x + y) + (z + w) = 360°

But (x + y) = (z + w) [Given]

∴ (x + y) + (x + y) = 360° or,

2(x + y) = 360°

or, (x + y) = 360° /2 = 180°

∴ AOB is a straight line.

Plz mrk as brainliest ❤