Question

Of the three angles of a triangle one is twice the smallest and another is thrice the smallest. Find the angles.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{be}\angle \mathrm{A},\angle \mathrm{B}\mathrm{and}\angle \mathrm{C}. \\ \mathrm{Let}\mathrm{the}\mathrm{smallest}\mathrm{angle}\mathrm{be}\angle \mathrm{C}. \\ \mathrm{Then}\angle \mathrm{A}=2\angle \mathrm{C}\mathrm{and}\angle \mathrm{B}=3\angle \mathrm{C} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{angle}\mathrm{sum}\mathrm{property},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180° \\ \Rightarrow 2\angle \mathrm{C}+3\angle \mathrm{C}+\angle \mathrm{C}=180° \\ \Rightarrow 6\angle \mathrm{C}=180° \\ \Rightarrow \angle \mathrm{C}=30° \\ \mathrm{Then}\angle \mathrm{A}=2\times 30°=60° \\ \mathrm{and}\angle \mathrm{B}=3\times 30°=90° \\ \therefore \mathrm{The}\mathrm{angles}\mathrm{are}30°,60°\mathrm{and}90°. \end{gathered}$$