Question

In a ∆ABC, if 3∠A = 4 ∠B = 6 ∠C, calculate the angles.

Answer 1

Let 3∠A = 4 ∠B = 6 ∠C = x
Then, we have:
$$\begin{gathered} \angle \mathrm{A}=\frac{\mathrm{x}}{3},\angle \mathrm{B}=\frac{\mathrm{x}}{4},\angle \mathrm{C}=\frac{\mathrm{x}}{6} \\ \mathrm{But},\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180° \\ \therefore \frac{\mathrm{x}}{3}+\frac{\mathrm{x}}{4}+\frac{\mathrm{x}}{6}=180° \\ \mathrm{or}\frac{4\mathrm{x}+3\mathrm{x}+2\mathrm{x}}{12}=180° \\ \mathrm{or}9\mathrm{x}=180°\times 12=2160° \\ \mathrm{or}\mathrm{x}=240° \\ \therefore \angle \mathrm{A}=\frac{240}{3}=80°,\angle \mathrm{B}=\frac{240}{4}=60°,\angle \mathrm{C}=\frac{240}{6}=40° \end{gathered}$$