Question

Prove that when two lines intersect each other the vertically opposite angle are equal

Answer 1

Since u said they form 90degree......the other adjacent angle is also 90 and the other angle adjacent to that angle will also be 90 degree

Answer 2

Step-by-step explanation:

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