Question

In a ∆ABC, if 2∠A = 3∠B = 6∠C, calculate ∠A, ∠B and ∠C.

• A. 90°, 60°, 30°
• B. 120°, 40°, 20°
• C. 100, 70°, 10°
• D. 90°, 70°, 20°

Answer 1

The correct option is A 90°, 60°, 30°

Suppose, 2∠A = 3∠B = 6∠C = x°
Then, ∠A = $\frac{x}{2}$∘
∠B =$\frac{x}{3}$ and ∠C = $\frac{x}{6}$

Sum of the angles of any triangle is 180°.
∠A +∠B +∠C = 180°
$\Rightarrow \frac{x}{2}+\frac{x}{3}+\frac{x}{6}=180°$
$\Rightarrow \frac{3x+2x+x}{6}=180°$
$\Rightarrow \frac{6x}{6}=180°\Rightarrow x=180°$

$\therefore \angle A=\frac{180°}{2}=90°$
$\angle B=\frac{180°}{3}=60°$
$\angle C=\frac{180°}{6}=30°$