Question

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In a ∆ABC, If 2∠A = 3∠B = 6∠C, then ∠B = ?

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer 1

$$\begin{gathered} \begin{array}{l}\left(c\right)60° \\ Given: \\ 2\angle A=3\angle B \\ \angle A=\frac{3}{2}\angle B...\left(\mathrm{i}\right) \\ 3\angle B=3\angle C \\ \angle C=\frac{1}{2}\angle B...\left(\mathrm{ii}\right)\\ \end{array} \\ \angle A+\angle B+\angle C=180° \\ \begin{array}{l}\text{=>}\frac{3}{2}\angle \text{B}+\angle \text{B}+\frac{1}{2}\angle \text{B}={\text{180°}}^{}\\ \text{=>}(\frac{3}{2}+1+\frac{1}{2})\angle \text{B}=\text{180°}\\ \text{=>}\frac{6}{2}\angle \text{B}=180°\\ \text{=>}\angle \text{B}=\frac{180°}{3}=60°\end{array} \end{gathered}$$