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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