Question

In Fig. 70, if AB || CD, then the values of x and y are
(a) x = 24, y = 48
(b) x = 34, y = 68
(c) x = 24, y = 68
(d) x = 34, y = 48

Answer 1

∠AGE + ∠BGE = 180° [Linear pair angles]
⇒ 121° + ∠BGE = 180°
⇒ ∠BGE = 59°
Since, AB || CD
∴ ∠BGE = ∠GHD = 59° [Corresponding angles]
⇒ x° + 25° = 59°
⇒ x = 34
In △GHI
∠GHI + ∠GIH + ∠HGI = 180° [Angle sum property of triangle]
⇒ 34° + 78° + y° = 180°
⇒ y = 68
Hence, the correct answer is option (b).