Question

In Fig. 107, if AOBand COD are straight lines, then
(a) x = 29, y = 100
(b) x = 110, y = 29
(c) x = 29, y = 110
(d) x = 39, y = 110

Answer 1

∠AOD + ∠BOD = 180^∘ [Linear pair angles]
⇒ y^∘ + 70^∘ = 180^∘
⇒ y^∘ = 110^∘
⇒ y = 110
Now, ∠AOC = ∠BOD = 70^∘ [Vertically opposite angles]
Now, ∠AOC + ∠COE + ∠EOB + ∠BOD + ∠AOD = 360^∘ [Complete angle]
⇒ 70^∘ + 28^∘ + (3x − 5)^∘ + 70^∘ + 110^∘ = 360^∘
⇒ (3x)^∘ + 273^∘ = 360^∘
⇒ 3x = 87
⇒ x = 29
Hence, the correct answer is option (c).