In Fig. 100, AB || CO and EF is a transversal intersecting AB and CD at P and Q respective. The measure of ∠OOP is
(a) 65
(b) 25
(c) 115
(d) 105

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Solution

∠BPE = ∠APQ = (5x − 10)^∘ [Vertically opposite angles]
Since, AB || CD
∴ ∠APQ + ∠CQP = 180^∘ [Angles on the same side of a transversal line are supplementary]
⇒ (5x − 10)^∘ + (3x − 10)^∘ = 180^∘
⇒ 8x − 20 = 180
⇒ 8x = 200
⇒ x = 25
∴ ∠BPE = (5 × 25 − 10)^∘ = 115^∘
Now, ∠BPE = ∠DQP = 115^∘ [Corresponding angles]
Hence, the correct answer is option (c).

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In Fig. 100, AB || CO and EF is a transversal intersecting AB and CD at P and Q respective. The measure of ∠OOP is (a) 65 (b) 25 (c) 115 (d) 105

In Fig. 100, AB || CO and EF is a transversal intersecting AB and CD at P and Q respective. The measure of ∠OOP is
(a) 65
(b) 25
(c) 115
(d) 105