The value of x is :

1. 2

2. 3

3. 1

4. none of these

In Δ AOB and Δ DOC

⇒ ∠AOB = ∠DOC (Vertically opposite angles are equal)

⇒ ∠BAO = ∠DCO (Corresponding angles are equal)

⇒ ∠ABO = ∠CDO (Corresponding angles since AB ∥ CD and BD is a transversal)

∴ Δ AOB ∼ Δ COD (By AAA postulates)

We know that,

Corresponding sides of similar triangles are proportional.

$\therefore \dfrac{OB}{OD} = \dfrac{AB}{CD}\\[1em] \Rightarrow \dfrac{3 }{4} = \dfrac{x + 1}{x + 2}\\[1em] \Rightarrow 3(x + 2) = 4(x + 1)\\[1em] \Rightarrow 3x + 6 = 4x + 4\\[1em] \Rightarrow 4x - 3x = 6 - 4\\[1em] \Rightarrow x = 2\\[1em]$

Hence, option 1 is the correct option.