Question

In ∆ABC, if 3∠A = 4 ∠B = 6 ∠C, calculate ∠A, ∠B and ∠C.

Answer 1

Let $3\angle A=4\angle B=6\angle C=x°$.
Then,
$$\begin{gathered} \angle A={\left(\frac{x}{3}\right)}^{°},\angle B={\left(\frac{x}{4}\right)}^{°}\text{and}\angle C={\left(\frac{x}{6}\right)}^{°} \\ \therefore \frac{x}{3}+\frac{x}{4}+\frac{x}{6}=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 4x+3x+2x=2160° \\ \Rightarrow 9x=2160° \\ \Rightarrow x=240° \end{gathered}$$
Therefore,
$\angle A={\left(\frac{240}{3}\right)}^{°}=80°,\angle B={\left(\frac{240}{4}\right)}^{°}=60°\text{and}\angle C={\left(\frac{240}{6}\right)}^{°}=40°$