Question

in fig AB||CD find the value of x​

Answer 1

In the given question,

We know that;

Since AB || CD,

• ∠OCD = ∠OAB      (∵ Alternate Interior Angles)
• ∠ODC = ∠OBA      (∵ Alternate Interior Angles)
• ∠DOC = ∠AOB      (∵ Vertically Opposite Angles)

By AAA similarity,

ΔOCD ∼ ΔOBA

So,

$\sf{\dfrac{OC}{OB} = \dfrac{OD}{OA}}$

Since ∠OCD = ∠OAB

OD = OB     (∵ Sides opposite to equal angles are equal)

⇒ (3x - 1) = (5x - 3)

⇒ -1 + 3 = 5x - 3x

⇒ 2x = 2

∴ x = 1

Additional Information:

• Alternate Interior Angles states that 2 angles lying on the either side of the transversal are equal.
• Vertically Opposite Angles states that 2 opposite angles on 2 straight lines are equal