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# In the figure shown, what is the value of x?

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Manager
Joined: 20 Aug 2009
Posts: 105
In the figure shown, what is the value of x? [#permalink]

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31 Aug 2009, 04:29
1
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Difficulty:

65% (hard)

Question Stats:

62% (02:50) correct 38% (01:25) wrong based on 37 sessions

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

(1) The length of line segment QR is equal to the length of line segment RS

(2) The length of line segment ST is equal to the length of line segment TU

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-figur ... 25923.html
[Reveal] Spoiler: OA
Senior Manager
Joined: 27 May 2009
Posts: 268
Re: In the figure shown, what is the value of x? [#permalink]

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31 Aug 2009, 06:07
6
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C it is
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Manager
Joined: 20 Aug 2009
Posts: 105
Re: In the figure shown, what is the value of x? [#permalink]

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31 Aug 2009, 06:11
Thanks and kudos!
I've seen a similar problem before, but forgot...
Manager
Joined: 04 May 2009
Posts: 67
Location: Astoria, NYC
Re: In the figure shown, what is the value of x? [#permalink]

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02 Sep 2009, 06:18
Intially I couldn't see how you got angle 1 + angle 6 to be 90.....but I got to open my eyes to see the bigger picture. Good explanation.
Definitely agree with C.
Manager
Joined: 15 Jun 2009
Posts: 153
Re: In the figure shown, what is the value of x? [#permalink]

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04 Sep 2009, 10:08
IMO C..too...gr8 effort ...clicking the image on web cam...
n thx...i m taking angles as RQS.....RSQ....taking 1,2,3, makes problem more easy..
Manager
Status: what we want to do, do it as soon as possible
Joined: 24 May 2010
Posts: 110
Location: Vietnam
WE 1: 5.0
Re: In the figure shown, what is the value of x? [#permalink]

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19 Mar 2011, 03:16
1
KUDOS
it is C:
(1) <R + <T = 90 in which:

(2) <R = 180 - <RQS - <RSQ = 180 - 2<RSQ (as RQ = RS)
(3) <T = 180 - <UST - <SUT = 180 - 2<UST ( as ST = TU)

(1) + (2) + (3):
180 - 2<RSQ + 180 - 2<UST = 90
=>360 - 2(<RSQ + <UST) = 90
=> 360 - 2 (180 -x) = 90
=> x= 45
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Math Expert
Joined: 02 Sep 2009
Posts: 39728
Re: In the figure shown, what is the value of x? [#permalink]

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13 Jun 2017, 23:12

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

$$x+\angle{QSR}+\angle{UST}=180$$ (straight line =180) and $$\angle{R}+\angle{T}=90$$ (as PRT is right angle)

(1) The length of line segment QR is equal to the length of line segment RS --> triangle QRS is isosceles --> $$\angle{RQS}=\angle{QSR}=\frac{180-\angle{R}}{2}$$ (as $$\angle{RQS}+\angle{QSR}+\angle{R}=180$$ --> $$2*\angle{QSR}+\angle{R}=180$$ --> $$\angle{QSR}=\frac{180-\angle{R}}{2}$$). Not sufficient.

(2) The length of line segment ST is equal to the length of line segment TU --> triangle UST is isosceles --> $$\angle{SUT}=\angle{UST}=\frac{180-\angle{T}}{2}$$. Not sufficient.

(1)+(2) $$x+\angle{QSR}+\angle{UST}=180$$ --> $$x+\frac{180-\angle{R}}{2}+\frac{180-\angle{T}}{2}=180$$ --> $$x+\frac{360-(\angle{R}+\angle{T})}{2}=180$$ --> since $$\angle{R}+\angle{T}=90$$ --> $$x+\frac{360-90}{2}=180$$ --> $$x=45$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-figur ... 25923.html
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Re: In the figure shown, what is the value of x?   [#permalink] 13 Jun 2017, 23:12
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