We are given that AB || CD and ∠OAB = 58° and ∠OCD = 42°.
Construction: Draw a line PQ || AB || CD
To find: x
PQ || AB (by construction)
⇒ ∠AOP = ∠OAB = 58° (alternate angle)
∴ ∠COP = ∠OCD = 42° (alternate angle)
∴ ∠AOC = ∠AOP + ∠COP = 58° + 42°
⇒ ∠AOC = 100°
Thus, reflex ∠AOC
x = 360° – ∠AOC
= 360° – 100° = 260°
Hence, x = 260°