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# Can anyone suggest the right approach .

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Director
Joined: 09 Aug 2006
Posts: 525
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Can anyone suggest the right approach . [#permalink]  06 Nov 2006, 07:02
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Can anyone suggest the right approach ..
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Manager
Joined: 01 Nov 2006
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The right approach is to assume both are true and then start labeling everything.

If RS = RQ, then Triangle RQS is isoceles so angle RQS = angle RSQ. Call this angle t. Now Angle SRQ = 180 - 2t.

Similarly, If TS = TU, then Triangle STU is isoceles so angle TUS = angle TSU. Call this angle p. Now Angle STU = 180 - 2p.

Now looking at the big triangle

180 = angle P + angle R + angle T

= 90 + (180 - 2t) + (180 - 2p)

which means 270 = 2*(p+t) or (p+t) = 135

Looking back at the original question Angle QSU + p + t = 180
so Angle QSU = 180 - (p+t) = 180 - 135 = 45

That neither individually is sufficient should be clear just by moving around angles p and t in your head.
VP
Joined: 15 Jul 2004
Posts: 1473
Schools: Wharton (R2 - submitted); HBS (R2 - submitted); IIMA (admitted for 1 year PGPX)
Followers: 17

Kudos [?]: 116 [0], given: 13

180-2a + 180 - 2b = 90 (assuming a and b are the angles in the two isoceles triangs)

so a+b = 135
and a + b + x = 180 So X can be determined.

Need both.
Senior Manager
Joined: 23 May 2005
Posts: 266
Location: Sing/ HK
Followers: 1

Kudos [?]: 19 [0], given: 0

Missing out on a geometry concept for sure...

dwivedys, 2 questions:

(1) why can you equate angle R and angle T to 90?
(2) why can you equate a+b+x to 180?
_________________

Impossible is nothing

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