In Fig. 99, AB || CD and EF is a transversal intersecting ABand CO at Pand Q respectively. The measure of ∠DPQ is
(a) 100^∘
(b) 80^∘
(c) 110^∘
(d) 70^∘

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Solution

∠BQF = ∠AQP = (4x)^∘ [Vertically opposite angles]
Since, AB || CD
∴ ∠AQP + ∠CPQ = 180^∘ [Angles on the same side of a transversal line are supplementary]
⇒ (4x)^∘ + (5x)^∘ = 180^∘
⇒ 9x = 180
⇒ x = 20
∴ ∠BQF = (4 × 20)^∘ = 80^∘
Now, ∠BQF = ∠DPQ = 80^∘ [Corresponding angles]
Hence, the correct answer is option (b).

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