Question

In $△$MNK, if $\angle$M + $\angle$N = 125$°$ and $\angle$M, $\angle$N and $\angle$K.

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{MNK},\angle \mathrm{M}+\angle \mathrm{N}=125° \\ \angle \mathrm{M}+\angle \mathrm{K}=113° \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{angle}\mathrm{sum}\mathrm{property},\mathrm{we}\mathrm{have}: \\ \angle \mathrm{M}+\angle \mathrm{N}+\angle \mathrm{K}=180° \\ \Rightarrow 125°+\angle \mathrm{K}=180°\left(\mathrm{Given}\right) \\ \Rightarrow \angle \mathrm{K}=55°...\left(1\right) \\ \mathrm{Also},\angle \mathrm{M}+\angle \mathrm{K}=113° \\ \Rightarrow \angle \mathrm{M}+55°=113°\left[\mathrm{From}\right(1\left)\right] \\ \Rightarrow \angle \mathrm{M}=58°....\left(2\right) \\ \mathrm{and}\angle \mathrm{N}=125°-\angle \mathrm{M}\left(\mathrm{Given}\right) \\ \Rightarrow \angle \mathrm{N}=125°-58°\left[\mathrm{From}\right(2\left)\right] \\ \Rightarrow \angle \mathrm{N}=67° \\ \mathrm{Thus},\angle \mathrm{M}=58°,\angle \mathrm{N}=67°\mathrm{and}\angle \mathrm{K}=55° \end{gathered}$$