Question

Find the value of 'x' in each of the following figures.

Answer 1

$$\begin{gathered} \mathrm{Here},\angle \mathrm{TEN}+\angle \mathrm{NEM}=180°(\mathrm{Linear}\mathrm{pair}) \\ \Rightarrow 100°+\angle \mathrm{NEM}=180° \\ \Rightarrow \angle \mathrm{NEM}=80°...\left(\mathrm{i}\right) \\ \mathrm{In}△\mathrm{ENM},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{EMR}=\angle \mathrm{NEM}+\angle \mathrm{MNE} \\ \Rightarrow \angle \mathrm{NEM}+x=140°(\mathrm{Exterior}\mathrm{angle}\mathrm{property}) \\ \Rightarrow 80°+x=140°\left[\mathrm{From}\right(\mathrm{i}\left)\right] \\ \Rightarrow x=60° \end{gathered}$$