In triangle DEF shown below, points A, B and C are taken on DE, DF and EF respec

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In triangle DEF shown below, points A, B and C are taken on DE, DF and EF respectively such that EC = AC and CF = BC. $∠$ D = 40 $^{\circ}$ then what is $∠$ ACB in degrees?(CAT 2001)

Options:

A . 140

^{\circ}

B . 70

^{\circ}

C . 100

^{\circ}

D . None of these

Answer: Option C
:
C

Option (c)

The angle in question is p

p+180-2x+180-2y=180 $^{\circ}$

thus p-2(x+y)= 180 $^{\circ}$ ……………..(1)

also, BDX = x+y (exterior angle= sum of 2 interior angles not adjacent to it)

x+y= 140 $^{\circ}$ ………(2)

using the 2 statements, p= 100 $^{\circ}$

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