In the given figure, the value of x is:

1. 15

2. 30

3. 36

4. 40

In Δ AOB and Δ DOC

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

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

⇒ ∠ABO = ∠CDO (Alternate angles are equal)

∴ Δ AOB ∼ Δ COD (By AAA postulate)

We know that,

Corresponding sides of similar triangles are proportional.

$\therefore \dfrac{AO}{CO} = \dfrac{OB}{OD}\\[1em] \Rightarrow \dfrac{18}{12} = \dfrac{x}{20}\\[1em] \Rightarrow x = \dfrac{18 \times 20}{12}\\[1em] \Rightarrow x = \dfrac{360}{12}\\[1em] \Rightarrow x = 30$

Hence, option 2 is the correct option.