In a ΔABC, if ∠A - ∠B = 33° and ∠B - ∠C = 18°, find the measure of each angle of the triangle.
Let the three angles of a triangle be ∠A, ∠B, ∠C
Given, ∠A - ∠B = 33°
⇒ ∠A = ∠B + 33°
∠B - ∠C = 18°
⇒ ∠C = ∠B – 18°
Now,
∠A + ∠B + ∠C = 180° [Sum of all angles of a triangle = 180°]
⇒ ∠B + 33° + ∠B + ∠B – 18° = 180°
⇒ 3∠B = 180° - 15°
⸫ ∠B = 55°
⸫ ∠A = ∠B + 33° = 88°
⸫ ∠C = ∠B – 18° = 37°