Question

In Fig. 96, if AB, CD and EF are straight lines, then x + y + z =
(a) 180
(b) 203
(c) 213
(d) 134

Answer 1

∠DAE + ∠BAD + ∠BAF = 180^∘ [EAF is a straight line]
⇒ 3x^∘ + 49^∘ + 62^∘ = 180^∘
⇒ 3x^∘ + 111^∘ = 180^∘
⇒ 3x^∘ = 69^∘
⇒ 3x = 69
⇒ x = 23
Now, ∠CAE + ∠CAF = 180^∘ [∵ EAF is a straight line]
⇒ z^∘ + y^∘ = 180^∘
⇒ z + y = 180
Now, x + y + z = 23 + 180 = 203
Hence, the correct answer is option (b).