Question

Il prove that,
Theorem - The opposite ongle
formed
by
two
jotersecting on line are of equal mesure​

Answer 1

Answer:

Proof :

If two lines intersect each other, then the vertically opposite angles are equal.

In the statement above, it is given that ‘two lines intersect each other’. So, let AB and CD be two lines intersecting at O as shown in Fig. 6.8. They lead to two pairs of vertically opposite angles, namely,

(i) ∠ AOC and ∠ BOD (ii) ∠ AOD and ∠ BOC.

We need to prove that ∠ AOC = ∠ BOD and ∠ AOD = ∠ BOC.

Now, ray OA stands on line CD.

Therefore, ∠ AOC + ∠ AOD = 180° (Linear pair axiom) ………..(1)

Can we write ∠ AOD + ∠ BOD = 180°? (Linear pair axiom)……………(2)

From (1) and (2), we can write

∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD

This implies that ∠ AOC = ∠ BOD

Similarly, it can be proved that ∠AOD = ∠BOC

Answer 2

$\large{\bold{\underline{\underline{ANSWER:}}}$

let ∠DOA = x

∠DOA + ∠AOB = 180° (linear pair)

∠AOB = 180-x

now, ∠AOB+∠BOC = 180

∠BOC = 180-∠AOB = 180-(180-x) =180-180+x = x

now, ∠DOA is opposite to ∠BOC

and ∠DOA = x = ∠BOC

therefore, The opposite angle  formed  by  two  intersecting on line are of equal measure​.

(refer to the attachment.)

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