Question

In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.

Answer 1

According to the question,

Measure of ∠A = ∠B – 40°

Measure of ∠C = ∠B – 40° + 50°

We know that, the sum of all three angles in a triangle is equal to 180°.

i.e. ∠A + ∠B + ∠C = 180°

⇒ (∠B – 40°) + ∠B + (∠B – 40° + 50°) = 180°

⇒ 3∠B – 30° = 180°

⇒ 3∠B = 210°

∴ ∠B = `210^circ/3` = 70°

So, the measure of ∠A = 70° – 40° = 30°.