Question

In Fig. 105, if AOB and COD are straight lines. Then, x + y =
(a) 120
(b) 140
(c) 100
(d) 160

Answer 1

∠AOD + ∠BOD = 180^∘ [Linear pair angles]
⇒ (7x − 20)^∘ + 3x^∘ = 180^∘
⇒ 7x − 20 + 3x = 180
⇒ 10x = 200
⇒ x = 20
∴ ∠AOD = (7 × 20 − 20)^∘ = 120^∘
Now∠AOD = ∠BOC = 120^∘ [Vertically opposite angles]
∴ y = 120
Now, x + y = 20 + 120
= 140
Hence, the correct answer is option (b).