Question

In the given figure of $△ABC$, let $\angle A={50}^o,B={60}^o,$ and $C={70}^o$. If mid-point of side $AB,BC$ and $CA$ are $D,E$ and $F$ respectively then find $\angle DEF$

Answer 1

REF.Image.

As line joining mid-

points of two sides

of triangle is parallel

to third side

$\Rightarrow DF\parallel BC\Rightarrow \angle AFD=\angle ACB={70}^{\circ }$

Similarly $\angle ADF={60}^{\circ }$

Similarly$EF\parallel AB$

$\Rightarrow FEC={60}^{\circ }$

Similarly $\angle DEB={70}^{\circ }$

By linear angle property

$70+60+\angle DEF={180}^{\circ }$

$\Rightarrow \angle DEF={50}^{\circ }$