Question

In Fig. 65, if AB || CE, then the values of x and y are
(a) x = 26, y = 144
(b) x = 36, y = 154
(c) x = 154, y = 36
(d) x = 144, y = 26

Answer 1

∠DCA + ∠ACB = 180° [Linear angles]
⇒ 134° + ∠ACB = 180°
⇒ ∠ACB = 46°
Now, In △ABC
∠BAC + ∠ACB+ ∠ABC = 180° [Angle sum property of triangle]
⇒ 62° + 46° + 2x° = 180°
⇒ 2x° = 72°
⇒ x = 36
Since, AB || CE
∴ ∠ECB = ∠CBA= (2x)° = (2 × 36)° = 72° [Alternate angles]
Now, ∠DCE + ∠ECB = 180° [Linear angles]
⇒ y° + 72° = 180°
⇒ y = 108
Disclaimer: No Option is correct