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In the figure above, STVW is a square, SX and YZ intersect at point W,

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In the figure above, STVW is a square, SX and YZ intersect at point W,  [#permalink]

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30 Oct 2018, 03:32
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Difficulty:

65% (hard)

Question Stats:

52% (02:19) correct 48% (02:29) wrong based on 62 sessions

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Note: Figure not drawn to scale.

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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In the figure above, STVW is a square, SX and YZ intersect at point W,  [#permalink]

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Updated on: 30 Oct 2018, 23:42
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

from given fig W would be 90
and each of a would be 22.5
a and B are opposite , b would be ~40 ie B..

Originally posted by Archit3110 on 30 Oct 2018, 03:44.
Last edited by Archit3110 on 30 Oct 2018, 23:42, edited 1 time in total.
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Re: In the figure above, STVW is a square, SX and YZ intersect at point W,  [#permalink]

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30 Oct 2018, 04:26
Bunuel wrote:
Note: Figure not drawn to scale.

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

Attachment:

STVW is a square. so $$\angle$$UVW = $$90^o$$.
So $$UV^2+VW^2 = UW^2$$, given UV=l & UW = 2l;
=> $$l^2 + VW^2 = (2l)^2$$
=> $$VW = \sqrt{3}$$
so $$\triangle UVW$$ is 1: $$\sqrt{3}$$: 2 triangle($$30^o:60^o:90^o$$) => so $$\angle VWU = 30^o$$ => $$\angle UWS = 90^o - 30^o = 60^o = 3a$$ => $$\angle 2a = 2*20^o = 40^o= b$$
Ans: B
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Re: In the figure above, STVW is a square, SX and YZ intersect at point W,  [#permalink]

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30 Oct 2018, 04:29
b = 2a (Vertically Opposite Angles)
Angle V = 90 degrees.
In Triangle WVU, UW = 2UV.
Angle VWU = 30 degrees ( 30-60 -90)
Angle UWS = 3a = 90 - 30 = 60.
a = 20
b = 2a = 40.
Ans . b
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Re: In the figure above, STVW is a square, SX and YZ intersect at point W,  [#permalink]

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01 Nov 2018, 22:43
This might sound like an amateurish doubt, but I am unable to understand as to why is b not equal to 3a?
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In the figure above, STVW is a square, SX and YZ intersect at point W,  [#permalink]

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02 Nov 2018, 03:00
1
narendran1990 wrote:
This might sound like an amateurish doubt, but I am unable to understand as to why is b not equal to 3a?

Hi,

b = 2a ( Vertically opposite Angles).
The lines ZY and SX intersect at W.
At this point of intersection, two angles are formed Angle ZWS and Angle XWY.
These two angles are vertically opposite.
Hope it clears the doubt.
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Re: In the figure above, STVW is a square, SX and YZ intersect at point W,  [#permalink]

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02 Nov 2018, 03:24
Akshay_Naik wrote:
b = 2a (Vertically Opposite Angles)
Angle V = 90 degrees.
In Triangle WVU, UW = 2UV.
Angle VWU = 30 degrees ( 30-60 -90)
Angle UWS = 3a = 90 - 30 = 60.
a = 20
b = 2a = 40.
Ans . b

Could you explain me why angle VWU=30 degrees? I know that one side equal 90 but how do you the 2 others equal 30 and 60?

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Re: In the figure above, STVW is a square, SX and YZ intersect at point W,  [#permalink]

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02 Nov 2018, 04:02
malbash01 wrote:
Akshay_Naik wrote:
b = 2a (Vertically Opposite Angles)
Angle V = 90 degrees.
In Triangle WVU, UW = 2UV.
Angle VWU = 30 degrees ( 30-60 -90)
Angle UWS = 3a = 90 - 30 = 60.
a = 20
b = 2a = 40.
Ans . b

Could you explain me why angle VWU=30 degrees? I know that one side equal 90 but how do you the 2 others equal 30 and 60?

Hi,

If you consider Triangle UVW, it is given in the problem statement that UW is twice UV.
Consider UV as x, UW would become 2x. Now apply the Pythagoras Theorem.
4x(square) - x(square) = vw(square).
VW = (square root)3x.

Compare all the angles in triangles, the ratio would be 1:2: square root 3.
This tells us that Angle UWV is 30 and Angle WUV = 60.

Hope it solves the doubt,
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Re: In the figure above, STVW is a square, SX and YZ intersect at point W,  [#permalink]

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02 Nov 2018, 05:05
Akshay_Naik wrote:
malbash01 wrote:
Akshay_Naik wrote:
b = 2a (Vertically Opposite Angles)
Angle V = 90 degrees.
In Triangle WVU, UW = 2UV.
Angle VWU = 30 degrees ( 30-60 -90)
Angle UWS = 3a = 90 - 30 = 60.
a = 20
b = 2a = 40.
Ans . b

Could you explain me why angle VWU=30 degrees? I know that one side equal 90 but how do you the 2 others equal 30 and 60?

Hi,

If you consider Triangle UVW, it is given in the problem statement that UW is twice UV.
Consider UV as x, UW would become 2x. Now apply the Pythagoras Theorem.
4x(square) - x(square) = vw(square).
VW = (square root)3x.

Compare all the angles in triangles, the ratio would be 1:2: square root 3.
This tells us that Angle UWV is 30 and Angle WUV = 60.

Hope it solves the doubt,

Thank you!!

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Re: In the figure above, STVW is a square, SX and YZ intersect at point W,   [#permalink] 02 Nov 2018, 05:05
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