In Δ ABC, D,E and F are taken on AB, AC and BC respectively, so that EF=CF and

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In $Δ$ ABC, D,E and F are taken on AB, AC and BC respectively, so that EF=CF and DF=BF. If $∠$ A=40 $^{\circ}$ , then find $∠$ DFE?

Options:

A . 100

^{\circ}

B . 120

^{\circ}

C . 90

^{\circ}

D . 140

^{\circ}

Answer: Option A
:
A

Option (a)

Take DBF = a $^{\circ}$ and ECF = b $^{\circ}$ .
40 + a $^{\circ}$ + b $^{\circ}$ = 180 $\Rightarrow$ a $^{\circ}$ + b $^{\circ}$ = 140
DFB + EFC + DFE = 180 $\Rightarrow$ 180 – 2a $^{\circ}$ + 180 – 2b $^{\circ}$ + DFE = 180 $\Rightarrow$ 180 $^{\circ}$ – 2(a + b) = - DFE
DFE = 280 – 180 = 100 $^{\circ}$

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