Question

Read the following Two States which are taken as exam first if two line insert take each other then the vertically opposite angle are not equal second if a Ray stands on a line then the sum of two adjacent angles so formed in equal to 180 is this system of axiom concept justify your answer

Answer 1

Answer:

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.

hope it helps

mark brainlest