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In the figure above, STVW is a square. SX and YZ intersect a [#permalink]
07 May 2020, 06:05
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41% (02:46) correct
58% (01:25) wrong based on 24 sessions
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#greprepclub In the figure above, STVW is a square..jpg [ 32.36 KiB  Viewed 602 times ]
In the figure above, STVW is a square. SX and YZ intersect at point W, and UW is twice as long as UV. What is the value of b ? A. 20° B. 40° C. 60° D. 120° E. 180° Kudos for the right answer and explanation
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Re: In the figure above, STVW is a square. SX and YZ intersect a [#permalink]
07 May 2020, 21:45
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We know that STVW is a square, thus all angles must be 90. Consider triangle UVW, we're given that UW is twice as long as UV. In case of 306090 triangle only the hypotenous is twice the length of smaller side. Thus, angle VWU must be 30. Thus, 3a = 60, a = 20. We can see that YZ passes through a and b. Thus a+30+90+b = 180, 20+30+90+b = 180, b = 180140, b=40. Thus, option B.



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Re: In the figure above, STVW is a square. SX and YZ intersect a [#permalink]
08 Oct 2020, 09:09
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Correct Answer: b) 40 degrees
We know that STVW is a square. Let us assume that side of square is x => VW = x >(1) We are given that UW = 2UV > (2) Consider triangle UVW, Angle V is 90 degrees => UW^2 = UV^2 +VW^2 => From (2) and (1), (2UV)^2 = UV^2 +x^2 => 4UV^2  UV^2 = x^2 => 3UV^2 = x^2 => UV = x/√3
Now, given that UW = 2UV = 2X/√3 Consider that UV:VW:UW = x/√3 : X : 2X/√3 = 1 : √3. : 2 => UVW is 306090 triangle. => Angle VUW. = 60 Angle VWU = 30 This means that 3a = 30 = 90 => 3a = 60 => a =20
Since SX and YZ intersect at point W, Angle ZWS = Angle XWY => B = 2a => b= 40 degrees




Re: In the figure above, STVW is a square. SX and YZ intersect a
[#permalink]
08 Oct 2020, 09:09





