Question

In Fig. 97, if AB is parallel to CD, then the value of ∠BPE is
(a) 106°
(b) 76°
(c) 74°
(d) 84°

Answer 1

Since, AB || CD
∴ ∠BPQ = ∠PQC [Alternate interior angles]
⇒ (3x + 34)^∘ = (5x − 14)^∘
⇒ 3x + 34 = 5x − 14
⇒ 48 = 2x
⇒ x = 24
∴ ∠BPQ = (3 × 24 + 34)^∘ = 106^∘
∠BPQ + ∠BPE = 180^∘ [EF is a straight line]
⇒ 106^∘ + ∠BPE = 180^∘
⇒ ∠BPE = 74^∘
Hence, the correct answer is option (c).