Question

The value of (x) is ______.

Options

• 2

• 3

• 1

• none of these

Answer 1

The value of (x) is 2.

Explanation:

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.

∴ ODOB ​= CDAB​

⇒ `3/4​ = (x+1​)/(x+2)`

⇒ 3(x + 2) = 4(x + 1)

⇒ 3x + 6 = 4x + 4

⇒ 4x − 3x = 6 − 4

⇒ x = 2