Question

In Fig. 69, if AB || CD, then the values of x and y are
(a) x = 106, y = 307
(b) x = 307, y = 106
(C) x =107, y = 306
(d) x = 105, y = 308

Answer 1

In △CDE
∠CDE + ∠CED + ∠ECD = 180° [Angle sum property of triangle]
⇒ 53° + 53° + ∠ECD = 180°
⇒ ∠ECD = 74°
Since, AB || CD
∴ ∠ECD = ∠CGB = 74° [Corresponding angles]
Now, ∠CGB + ∠BGF = 180° [Linear pair angles]
⇒ 74° + x° = 180°
⇒ x = 106
Now, In △EGB
∠EGB + ∠BEG + ∠EBG = 180° [Angle sum property of triangle]
⇒ 74° + 53° + ∠EBG = 180°
⇒ ∠EBG = 53°
Now, ∠EBG + Reflex∠EBG = 360° [Complete angle]
⇒ 53° + y° = 360°
⇒ y = 307
Hence, the correct answer is option (a).