Question

In Fig. 101, AB || CD and EF is a transversal. The value of y − x is
(a) 30
(b) 35
(c) 95
(d) 25

Answer 1

Since, AB || CD
∴ ∠BPQ = ∠DQF [Corresponding angles]
⇒ (5x − 20)^∘ = (3x + 40)^∘
⇒ 5x − 20 = 3x + 40
⇒ 2x = 60
⇒ x = 30
∴ ∠BPQ = (5 × 30 − 20 )^∘ = 130^∘
Now, ∠APE = ∠BPQ [Vertically opposite angles]
⇒ 2y^∘ = 130^∘
⇒ y = 65
∴ y − x = 65 − 30 = 35
Hence, the correct answer is option (b).