emmak wrote:

Attachment:

The attachment **1.gif** is no longer available

In the figure above, what is the value of x?

(1) AD = AE = BE = CD = BC

(2) x = y

Figure attached

STAT1.

Consider Triangle BCD

sum of all three angles = 180

so, y + b + d + e = 180

Also, BC = CD

=> b = d + e

so, equation becomes

y + d + e + d + e = 180

y + 2d + 2e= 180 ... (1)

Consider traingle BCE

sum of all three angles = 180

so, a + c+ y + e = 180

Also, BC = BE

so, a = c+y

so, equation becomes

y + c + y+ c+ y = 180

3y + 2c = 180 ...(2)

Consider traingle ABC

sum of all three angles = 180

so, x + y + c+ d + e = 180 ...(3)

Consider traingle AEB

AE = EB

so, x = d ...(4)

Consider traingle ADC

AD = DC

so, x = c ...(5)

putting d=x (1) becomes

2x + y + 2e = 180 ...(6)

putting c=x in (2) becomes

2x + 3y = 180 ...(7)

putting c=x and d=x in (3) we have

3x+y+e=180 ...(8)

mutiply (8) by 2 and subtract from (6) we have

4x + y = 180 ...(9)

equating (7) and (9) we have

2x+ 3y = 4x+y

=> 2y = 2x

or x=y

putting x=y in (7) we have

5x= 180

x= 36

So, STAT1 is sufficient

STAT2

STAT2 is not sufficient as we dont have relationship between any other angles.

So, Answer will be A.

Will reply in sometime with a smaller and more geometric solution if i get in sometime!

Hope it helps!

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