In Fig. 71, if AB || CD, then the values of x, y and z are
(a) x = 56, y = 47, z = 77
(b) x = 47, y = 56, z = 77
(c) x = 77, y = 56, z = 47
(d) x = 56, y = 77, z = 47

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Solution

∠AFE + ∠EFG = 180° [Linear pair angles]
⇒ 124° + ∠EFG = 180°
⇒ ∠EFG = 56°
Since, AB || CD
∴ ∠EFG = ∠FHK = 56° [Corresponding angles]
⇒ x = 56
Now, ∠QKH + ∠GKH = 180° [Linear pair angles]
⇒ 103° + ∠GKH = 180°
⇒ ∠GKH = 77°
Since, AB || CD
∴ ∠EGF = ∠GKH = 77° [Corresponding angles]
⇒ y = 77
In △EHK
∠EHK + ∠EKH + ∠HEK = 180° [Angle sum property of triangle]
⇒ 56° + 77° + z° = 180°
⇒ z = 47
Hence, the correct answer is option (d).

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