Question

In Fig. 108, if AB || CD then the value of x is
(a) 87
(b) 93
(c) 147
(d) 141

Answer 1

Construction: Draw a line PQ parallel to AB which is also parallel to CD
∠FCD + Reflex∠FCD = 360^∘ (Complete angle)
⇒ ∠FCD + 273^∘ = 360^∘
⇒ ∠FCD = 87^∘
Since, PQ || CD
∴∠QFC + ∠FCD = 180^∘ (Angles on the same side of a transversal line are supplementary)
⇒ ∠QFC + 87^∘ = 180^∘
⇒ ∠QFC = 93^∘
Now, ∠ABF = ∠BFQ (Corresponding angles)
= ∠BFC + ∠QFC
= 54^∘ + 93^∘
= 147^∘
∴ x^∘ = 147^∘
⇒ x = 147
Hence, the correct answer is option (c).