In a ΔABC, if ∠ A - ∠ B = 33 ° and ∠ B - ∠ C = 18 ° , find the measure of each angle of the triangle.

Question

Philoid · Accepted Answer

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°