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

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In the parallelogram shown, what is the value of x?  [#permalink]

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New post 25 Oct 2015, 09:12
6
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A
B
C
D
E

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69% (00:59) correct 31% (01:17) wrong based on 1416 sessions

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Re: In the parallelogram shown, what is the value of x?  [#permalink]

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New post 25 Oct 2015, 09:51
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Bunuel wrote:
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In the parallelogram shown, what is the value of x?

(1) y = 2x
(2) x + z = 120


Kudos for a correct solution.

Attachment:
2015-10-25_2009.png


Given that the shape is a parallelogram, y+x=180 and y+z=180

Per statement 1, y=2x ---> 2x+x=180 ---> x=60. Sufficient.

Per statement 2, x+z=120 and y+z=180 ---> y-x=60 and with x+y=180 ---> x=60. Sufficient.

D is the correct answer.
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Re: In the parallelogram shown, what is the value of x?  [#permalink]

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New post 25 Oct 2015, 09:51
2
Bunuel wrote:
Image
In the parallelogram shown, what is the value of x?

(1) y = 2x
(2) x + z = 120


Kudos for a correct solution.

Attachment:
2015-10-25_2009.png


y+z= 180
x=z
(1) y = 2x
y+z=y+x = 180 => Know x => sufficient

(2) x + z = 120
x=z
=> Know x => sufficient

Ans: D
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Re: In the parallelogram shown, what is the value of x?  [#permalink]

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New post 26 Oct 2015, 02:26
1
Bunuel wrote:
Image
In the parallelogram shown, what is the value of x?

(1) y = 2x
(2) x + z = 120


Kudos for a correct solution.

Attachment:
2015-10-25_2009.png


IMO Answer is D

Statement 1 : y=2x , x+2x = 180 Sifficient.

Statement 2: y+z = 180, y+x=180 x=z , 2z = 120 , means , x=60 Sufficient.

NOTE: How does one can upload an attachment while answering to question :?
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Re: In the parallelogram shown, what is the value of x?  [#permalink]

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New post 26 Oct 2015, 04:17
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1
Opposite angles are equal in a Quadrilateral
so Angle X = Angle Z

1) Y = 2X. X + Y =180 so 3X=180 or X=60.
2) X+Z=120. X=Z so 2X=120 or X=60.

So D is the correct answer
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In the parallelogram shown, what is the value of x?  [#permalink]

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New post 06 Jan 2017, 00:46
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Bunuel wrote:
Image
In the parallelogram shown, what is the value of x?

(1) y = 2x
(2) x + z = 120


Kudos for a correct solution.

Attachment:
2015-10-25_2009.png

Propoerties of //gm:
A. Consectutive angles are supplementary. => y+x=180
B. Opposite angles are equal => z=x

1) y=2x; From A; 2x+x=180 => x=60 => Sufficient
2) x+z=120; From B; x=z=60 => Sufficient

D.
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Re: In the parallelogram shown, what is the value of x?  [#permalink]

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New post 11 Dec 2017, 14:40
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Hi All,

We're asked to find the value of angle X in the parallelogram.

When dealing with a parallelogram, there are a variety of math rules about that shape that you might find useful:
1) Opposite sides have equal length
2) Opposite angles are equal
3) The two angles on a 'side' of the shape will add up to 180 degrees.

1) Y = 2X

Since angle Y and angle X are on the same 'side', we know that Y + X = 180 degrees. With Fact 1, we are given a second equation to work with, so we clearly have a 'system' of equations (so you can figure out the values of X and Y). In this case, X = 60, Y = 120
Fact 1 is SUFFICIENT

2) X + Z = 120

Since X and Z are opposite angles, we know that they are equal. With the information in Fact 2, we now know that they are X = 60 and Z = 60.
Fact 2 is SUFFICIENT

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Re: In the parallelogram shown, what is the value of x?  [#permalink]

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New post 28 Jun 2018, 21:41
This Question is testing Two rules of a parallelogram:

Statement 1: consecutive angles are supplementary
Statement 1: opposites angles are equal.
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Re: In the parallelogram shown, what is the value of x?  [#permalink]

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Re: In the parallelogram shown, what is the value of x?   [#permalink] 13 Jul 2019, 13:22
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