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Difficult Geometry DS

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Difficult Geometry DS

by GMATpaduan » Sat Aug 04, 2007 1:09 pm
The answer is C - but can someone please explain why? Does the answer have something to do with similar triangles?

This is from GMATPrep (TM) Test.

Thanks.

File is attached.
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Geometry - DS - Test 1 #7.JPG
GOOD LUCK ALL!
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Source: — Data Sufficiency |
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by karthick451 » Thu Aug 09, 2007 7:21 am
I agree with the answer. it is C.

Here is my take

x + angle(RSQ) + angle(UST) = 180

x = 180 - (angle(RSQ) + angle(UST))

angle(RSQ) = (180 - angle(QRS)) /2
angle(UST) = (180 - angle(STU))/2

substituting

x = 180 - (90 +90 - (angle(QRS) + angle(STU))/2))
= 180 - (90 + 90 - 45)
= 45

hence.....
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