If two lines intersect then the vertically opposite angles are equal

Given two lines AB and CD intersect each other at the point O.

To prove: ∠1 = ∠3 and ∠2 = ∠4

Proof:

From the figure, ∠1 + ∠2 = 180° [Linear pair] → (1)

∠2 + ∠3 = 180° [Linear pair] → (2)

From (1) and (2), we get

∠1 + ∠2 = ∠2 + ∠3

∴ ∠1 = ∠3

Similarly, we can prove ∠2 = ∠4 also.