From the given figure, find angle MLN

Dear Student,
In these triangles two sides are proportional.
i.e.
$$\begin{gathered} \frac{MN}{BC}=\frac{{\displaystyle 10}}{4}=2.5 \\ \frac{{\displaystyle LN}}{AC}=\frac{{\displaystyle 9}}{3.6}=2.5 \\ \frac{ML}{AB}=\frac{11}{4.4}=2.5 \end{gathered}$$
 
And as we know that if all the  sides of two triangles are proportional then the two triangles are similar.
i.e. $△ ABC ~ △LMN$
In two similar triangles all corresponding internal angles are equal

i.e.
$$\begin{gathered} \angle A=\angle L \\ \angle B=\angle M \\ \angle C=\angle N \\ In △ABC \\ \angle A+\angle B+\angle C={180}^{\circ } \\ \angle A+{50}^{\circ }+{70}^{\circ }={180}^{\circ } \\ \angle A={180}^{\circ }-{120}^{\circ } \\ \angle A={60}^{\circ } \\ So, \\ \angle M={50}^{\circ } \\ \angle L={60}^{\circ } \\ \angle N={70}^{\circ } \\ \Rightarrow \angle MLN={60}^{\circ } \end{gathered}$$

Regards.