ABCD is trapezium, and the diagonals intersect at O... AO = x +5 , OC= x +3 , DO = x-2 and BO = x-1.

Find x if AB is parallel to DC.......

Given, ABCD is a trapezium having AB || DC.

Again, AO = x + 5, OC = x + 3,  OD = x – 2 and OB = x – 1

In ΔAOB & ΔDOC, we have

∠AOB = ∠DOC  [Vertically opposite angle]

∠OAB = ∠OCD  [Alternative interior angle]

⇒ ΔOAB ∼ ΔOCD  [AA similarity]

⇒ (x + 5) (x – 2) = (x – 1) (x + 3)

⇒ x² + 5x – 2x – 10 = x² – x + 3x – 3

⇒ x = 7