Question

In ∆ABC, if 2∠A = 3∠B = 6∠C, calculate the measure of ∠B.

Answer 1

In a ∆ABC, 2$\angle$A = 3$\angle$B = 6$\angle$C = x^o (say)

$$\begin{gathered} \mathrm{Therefore},\angle A=\frac{x°}{2} \\ \angle B=\frac{x°}{3} \\ \angle C=\frac{x°}{6} \\ \mathrm{By}\mathrm{angle}\mathrm{sum}\mathrm{property}\mathrm{in}∆ABC, \\ \angle A+\angle B+\angle C=180° \\ \Rightarrow \frac{x°}{2}+\frac{x°}{3}+\frac{x°}{6}=180° \\ \Rightarrow x°=180°\mathrm{Therefore},\angle B=\frac{x°}{3}=\frac{180°}{3}=60°. \end{gathered}$$