Question

In Fig. 109, if AB || CD then the value of x is
(a) 34
(b) 124
(c) 24
(d) 158

Answer 1

Construction: Draw a line PQ parallel to AB which is also parallel to CD
∠QEC + ∠ECD = 180^∘ [Angles on the same side of a transversal line are supplementary]
⇒ ∠QEC + 56^∘ = 180^∘
⇒ ∠QEC = 124^∘
Now, ∠BEQ + ∠QEC = ∠BEC
⇒ ∠BEQ + 124^∘ = 158^∘
⇒ ∠BEQ = 34^∘
Now, ∠ABE = ∠BEQ = 34^∘ [Corresponding angles]
∴ x^∘ = 34^∘
⇒ x = 34
Hence, the correct answer is option (a).