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In the figure above, STVW is a square. SX and YZ intersect a

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In the figure above, STVW is a square. SX and YZ intersect a [#permalink] New post 07 May 2020, 06:05
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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°

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[Reveal] Spoiler: OA

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Re: In the figure above, STVW is a square. SX and YZ intersect a [#permalink] New post 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 30-60-90 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 = 180-140, b=40. Thus, option B.
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Re: In the figure above, STVW is a square. SX and YZ intersect a [#permalink] New post 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 30-60-90 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
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In the figure above, STVW is a square. SX and YZ intersect a

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