Question

In Fig. 68, the values of x and y are
(a) x = 120, y = 150
(b) x = 110, y = 160
(c) x = 150, y = 120
(d) x = 110, y = 160

Answer 1

In △DEF
∠DEF + ∠DFE + ∠EDF = 180° [Angle sum property of triangle]
⇒ 110° + 40° + ∠EDF = 180°
⇒ ∠EDF = 30°
Now, ∠EDF + ∠FDA = 180° [Linear pair angles]
⇒ 30° + x° = 180°
⇒ x = 150
Now, ∠EDF = ∠ADB = 30° [Vertically opposite angles]
Now, In △ABD
∠ADB + ∠DAB + ∠ABD = 180° [Angle sum property of triangle]
⇒ 30° + 90° + ∠ABD = 180°
⇒ ∠ABD = 60°
Now, ∠ABD + ∠DBC = 180° [Linear pair angles]
⇒ 60° + y° = 180°
⇒ y = 120
Hence, the correct answer is option (c).