Question

In а ΔАВС, ∠C = 3∠B = 2(∠A + ∠B). Find the measure of each one of ∠A, ∠B and C.

Answer 1

Given: In triangle ABC, ∠C = 3∠B = 2(∠A + ∠B).

Step-wise calculation:

1. From ∠C = 3∠B and ∠C = 2(∠A + ∠B), equate: 3∠B = 2(∠A + ∠B).

2. Expand right side:

3∠B = 2∠A + 2∠B

3. Rearrange:

3∠B – 2∠B = 2∠A 

⇒ ∠B = 2∠A

4. Express all angles in terms of ∠A:

∠B = 2∠A

∠C = 3∠B

= 3(2∠A)

= 6∠A

5. Sum of angles:

∠A + ∠B + ∠C 

= ∠A + 2∠A + 6∠A

= 9∠A

= 180°

6. Solve:

∠A = `(180^circ)/9` 

= 20°

Then ∠B = 2 × 20°

= 40°

∠C = 6 × 20°

= 120°