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# Geometry DS problem

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Joined: 31 Jul 2006
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Geometry DS problem [#permalink]  23 Sep 2006, 11:53
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For the search: The length of line segment QR
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Joined: 06 May 2006
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C it is.

Take Angle QRS = r
Angle STU = t
Angle RSQ = a
Angle TSU = b

Now, you can see that a + b + x = 180 (The three angles on Line segment RST)

Case 1: QR = QS
We get r + 2a = 180
Insufficient

Case 2: TS = UT
We get t + 2b = 180
Insufficient

Combining, we get r + t + 2a + 2b = 360.
But r + t = 90 (Triangle RPT is a right angled triangle)
=> 2(a+b) = 270
=> a+b = 135

Now a + b + x = 180 => x = 45.
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