Question

Two angles of a triangle are equal and the third angle is greater than each of those angles by 30°. Determine all the angles of the triangle.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{two}\mathrm{equal}\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{be}\mathrm{x}. \\ \mathrm{Hence},\mathrm{the}\mathrm{third}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{will}\mathrm{be}(\mathrm{x}+30°). \\ \mathrm{Sum}\mathrm{of}\mathrm{all}\mathrm{the}\mathrm{three}\mathrm{angle}\mathrm{of}\mathrm{a}\mathrm{triangle}=180° \\ \therefore \mathrm{x}+\mathrm{x}+(\mathrm{x}+30°)=180° \\ \Rightarrow \mathrm{x}+\mathrm{x}+\mathrm{x}+30°=180° \\ \Rightarrow 3\mathrm{x}+30°=180° \\ \Rightarrow 3\mathrm{x}=180°-30° \\ \Rightarrow 3\mathrm{x}=150° \\ \Rightarrow \mathrm{x}=\frac{150°}{3} \\ \mathbf{\Rightarrow }\mathbf{x}\mathbf{=}\mathbf{50}\mathbf{°} \\ (\mathrm{x}+30°)=50°+30° \\ \mathbf{\Rightarrow }\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{30}\mathbf{°}\mathbf{)}\mathbf{=}\mathbf{80}\mathbf{°} \\ \mathrm{Hence},\mathrm{we}\mathrm{can}\mathrm{conclude}\mathrm{that}\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{are}50°,50°\mathrm{and}80°. \end{gathered}$$