Question

In the figure x = z and y = w the prover that AOB is a straight line.
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Answer 1

Step-by-step explanation:

Given in the figure...

$x = z \\ y = w$

Now we know that sum of total angle si 360

$x + y + z + w = 360 \\ \\ x + y + x + y = 360 \\ \\ 2x + 2y = 360 \\ \\ 2(x + y) = 360 \\ \\ x + y = \frac{360}{2} \\ \\ x + y = 180$

Here sum of two angles x and y at line AOB is equal to 180°

means it form a linear pair.

Hence AOB is stright line.

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 ❤