In the given figure, AB ||CD. Find the value of x.

X=45

Given AB||CD

Therefore, ∠BAC + ∠ACD = 180°

⇒ 75° + ∠ACD = 180°

⇒ ∠ACD = 105°_________________ (i)

∠ACD = ∠ECF = 105°[Opposite angles]

In triangle CEF,

⇒ ∠CEF + ∠EFC + ∠FCE = 180°

⇒ x + 30° + 105° = 180°

⇒ x + 135° = 180°

⇒ x = 45°