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Quantitaitve Aptitude
Geometry Set Ii
Question
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
∘
, then find
∠
DFE?
Options:
A
.
 100∘
B
.
 120∘
C
.
 90∘
D
.
 140∘
Answer: Option A
:
A
Option
(a)
Take DBF =
a
∘
and ECF =
b
∘
.
40 +
a
∘
+
b
∘
= 180
⇒
a
∘
+
b
∘
= 140
DFB + EFC + DFE = 180
⇒
180 – 2a
∘
+ 180 – 2b
∘
+ DFE = 180
⇒
180
∘
– 2(a + b) = - DFE
DFE = 280 – 180
= 100
∘
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