Question

The angles of a triangle are (2x – 30°),(3x – 40°) and ( x + 10°) Find the value of x .

Answer 1

∵ The sum of angles of a triangle = 180°

∴ (2x – 30°) + (3x – 40°) + ${\displaystyle (\frac{5}{2}x+10°)=180°}$

⇒ 2x - 30° + 3x - 40° + ${\displaystyle \frac{5}{2}}$x + 10° = 180°

⇒ 2x + 3x + ${\displaystyle \frac{5}{2}}$x - 70° + 10° = 180°

⇒ ${\displaystyle \frac{\text{4x}+\text{6x}+\text{5x}}{2}-60°=180°}$

⇒ ${\displaystyle \frac{15}{2}}$x = 180° + 60° = 240°

x = ${\displaystyle \frac{240°\times 2}{15}=32}$

∴ x = 32°