Question

In given figure, find $\angle F$

Answer 1

In triangles ABC and DEF, we have

$\frac{AB}{DF}=\frac{BC}{FE}=\frac{CA}{ED}=\frac{1}{2}$

Therefore, by SSS-criterion of similarity, we have

$△ABC\sim △DEF$

$\Rightarrow$ $\angle A=\angle D,\angle B=\angle F$ and $\angle C=\angle E$

$\Rightarrow$ $\angle D={80}^0,\angle F={60}^0$

Hence, $\angle F={60}^0$