Question

If the radian measure of two angles of a triangle r as given below. Find the radian measure and the degree measure of the third angle.
[i] 5 pie / 9 , 5 pie / 18.
[ii] 3 pie / 5 , 4 pie / 15.

Answer 1

$$\begin{gathered} \mathrm{i}) \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{sum}\mathrm{of}\mathrm{all}\mathrm{the}\mathrm{angles}\mathrm{in}\mathrm{a}\mathrm{triangle}\mathrm{is}\mathrm{\pi }\mathrm{radian}\mathrm{or}180\mathrm{degree} \\ \mathrm{So}\frac{5\mathrm{\pi }}{9}+\frac{5\mathrm{\pi }}{18}+\mathrm{third}\mathrm{angle}=\mathrm{\pi } \\ \mathrm{third}\mathrm{angle}=\mathrm{\pi }-\frac{10\mathrm{\pi }}{18}-\frac{5\mathrm{\pi }}{18}=\frac{18\mathrm{\pi }-15\mathrm{\pi }}{18}=\frac{\mathbf{\pi }}{\mathbf{6}}\mathbf{}\mathbf{radian} \\ =\frac{\mathrm{\pi }}{6}\times \frac{180}{\mathrm{\pi }}=30\mathrm{degree} \\ \mathrm{Similar}\mathrm{approach}\mathrm{will}\mathrm{be}\mathrm{for}\mathrm{the}\mathrm{second}\mathrm{part}. \end{gathered}$$