Mathematics

# In the given figure of $\triangle ABC$, 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 $\angle DEF$

##### SOLUTION
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
$70+60+\angle DEF = 180^{\circ}$
$\Rightarrow \angle DEF = 50^{\circ}$

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Subjective Medium Published on 09th 09, 2020
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