Question

In a △ABC, if ∠A − ∠B = 33° and ∠B − ∠C = 18°, then ∠B =
(a) 35°
(b) 45°
(c) 55°
(d) 25°

Answer 1

∠A − ∠B = 33° and ∠B − ∠C = 18°
⇒ ∠A = ∠B + 33° and ∠C = ∠B − 18°
Now, ∠A + ∠B + ∠C = 180° [Angle sum property of triangle]
⇒ ∠B + 33° + ∠B + ∠B − 18° = 180°
⇒ 3∠B + 15° = 180°
⇒ 3∠B = 165°
⇒ ∠B = 55°
Hence, the correct answer is option (d).