Question

In a ΔАBC, ∠A = x°, ∠B = (3x – 2)°, ∠C = y° and ∠C – ∠B = 9°. Find the three angles.

Answer 1

Given: In ΔABC, ∠A = x°, ∠B = (3x – 2)°, ∠C = y° and ∠C – ∠B = 9°.

Step-wise calculation:

1. Angle-sum:

x + (3x – 2) + y = 180 

⇒ 4x + y – 2 = 180

⇒ 4x + y = 182

2. Difference condition:

y – (3x – 2) = 9 

⇒ y – 3x + 2 = 9

⇒ y – 3x = 7

⇒ y = 3x + 7

3. Substitute:

4x + (3x + 7) = 182 

⇒ 7x + 7 = 182

⇒ 7x = 175

⇒ x = 25

4. ∠B = 3x – 2

= 3(25) – 2 

= 75 – 2

= 73

5. ∠C = y

= 3x + 7 

= 75 + 7 

= 82

6. Check: 25 + 73 + 82 = 180°.

∠A = 25°, ∠B = 73°, ∠C = 82°.