Question

in fig. if x + y+ z, then prove that AOB is a line

Answer 1

We know that ,
x + y = 180° (linear pair) ---------> ( i )
and ,
w + z = 180° (linear pair) ---------> ( ii )

From equation ( i ) and ( ii ), we have:
x + y + w + z = 180° + 180°
=>x + y x+ y = 360° { Since, x + y = w + z }
=>2x + 2y = 360°
=>2(x + y) = 360°
=>x + y = 360/2
=>x + y = 180°
therefore, AOB is a line.

$\mathfrak{\green{\huge{Be \:Brainly}}}$

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 ❤