Question

In Fig. 64, if AB || CD, the values of x and y are
(a) x = 21, y = 28
(b) x = 21, y = 38
(c) x = 38, y = 21
(d) x = 22, y = 38

Answer 1

∠AEC + ∠AEB = 180° [Linear angles]
⇒ 79° + ∠AEB = 180°
⇒ ∠AEB = 101°
Since, AB || CD
∠ABE = ∠ECD = 58° [Alternate angles]
Now, In △AEB
∠AEB + ∠EAB + ∠ABE = 180° [Angle sum property of triangle]
⇒ 101° + 58° + x° = 180°
⇒ x° = 21°
⇒ x = 21
Now, In △AEB
∠AEC + ∠CAE + ∠CEA = 180° [Angle sum property of triangle]
⇒ 79° + y° + 3x° = 180°
⇒ 79° + y° + 3(21)° = 180°
⇒ 79° + y° + 63° = 180°
⇒ y° = 38°
⇒ y = 38
Hence, the correct answer is option (b).