Question

The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°, find the three angles.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{first}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{be}\mathrm{x}. \\ \mathrm{Therefore},\mathrm{we}\mathrm{can}\mathrm{say}\mathrm{that}\mathrm{the}\mathrm{second}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{will}\mathrm{be}(\mathrm{x}+10°)\mathrm{and}\mathrm{the}\mathrm{third}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{will}\mathrm{be}(\mathrm{x}+10°+10°). \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{all}\mathrm{the}\mathrm{three}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{is}\mathrm{equal}\mathrm{to}180°. \\ \therefore \mathrm{x}+(\mathrm{x}+10°)+(\mathrm{x}+10°+10°)=180° \\ \Rightarrow \mathrm{x}+\mathrm{x}+\mathrm{x}+10°+10°+10°=180° \\ \Rightarrow 3\mathrm{x}+30°=180° \\ \Rightarrow 3\mathrm{x}=180°-30° \\ \Rightarrow 3\mathrm{x}=150° \\ \Rightarrow \mathrm{x}=\frac{150°}{3} \\ \Rightarrow \mathrm{x}=50° \\ \mathrm{Now},(\mathrm{x}+10°)=50°+10° \\ \Rightarrow (\mathrm{x}+10°)=60° \\ \mathrm{And},(\mathrm{x}+10°+10°)=50°+10°+10° \\ \Rightarrow (\mathrm{x}+10°+10°)=70° \\ \mathrm{Hence},\mathrm{we}\mathrm{can}\mathrm{say}\mathrm{that}\mathrm{the}\mathrm{three}\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{are}50°,60°\mathrm{and}70°. \end{gathered}$$