Question

In a △ABC,if ∠A + ∠B = 150° and ∠B + ∠C = 75°, then ∠B =
(a) 35°
(b) 45°
(c) 55°
(d) 25°

Answer 1

∠A + ∠B + ∠C = 180° [Angle sum property of triangle]
⇒ 150° + ∠C = 180°
⇒ ∠C = 30°
Now, ∠B + ∠C = 75°
⇒ ∠B + 30° = 75°
⇒ ∠B = 45°
Hence, the correct answer is option (b).