Question

In Fig. 111, if AB || CO then x =
(a) 154
(b) 139
(c) 144
(d) 164

Answer 1

Construction: Draw a line PQ parallel to AB which is also parallel to CD
Since, PQ || AB
∴ ∠AME + ∠QEM = 180^∘ [Angles on the same side of a transversal line are supplementary]
⇒ 139^∘ + ∠QEM = 180^∘
⇒ ∠QEM = 41^∘
Now, ∠QEM + ∠DEQ = ∠MED
⇒ 41^∘ + ∠DEQ = 67^∘
⇒ ∠DEQ = 26^∘
Now, ∠PED + ∠DEQ = 180^∘ [Linear Pair angles]
⇒ ∠PED + 26^∘ = 180^∘
⇒ ∠PED = 154^∘
Since, PQ || AB
∴ x^∘ = ∠PED [Corresponding angles]
⇒ x^∘ = 154^∘
⇒ x = 154
Hence, the correct answer is option (a).