GmatPrep DS - Geom

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GmatPrep DS - Geom

by rkumar » Mon Jul 28, 2008 4:14 am
We have to find the value of x inside a traingle. The answer is C. I need explaination for this. I have attached the question
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GMAT DS.GIF
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by bha » Mon Jul 28, 2008 6:31 am
Let PQS = a
PUS=b
RQS=RSQ=y...by statement 1(Triangle RQS is Isosceles triangle)
TSU=TUS=z...by statement 2(Triangle TSU is Isosceles triangle)

90+a+b+x= 360
a+b+x = 270 .........(1)


y+a= 180
y = 180-a...........(2)

b+z=180
z = 180-b...........(3)


y+x+z = 180
substituting y and z using eqns (2) and (3)
180-a+x+180-b=180
-a-b+x=-180..........(4)

Adding (1) and (4)
2x= 90
x=45

C is answer.

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by rkumar » Mon Jul 28, 2008 8:06 am
Thanks

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by jmtkrs10 » Sat Aug 09, 2008 11:27 pm
In step 4, why is y+x+z = 180?