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

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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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

Final Answer:

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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

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

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

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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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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Solution:

We need to determine the value of x. Recall that in a parallelogram, opposite angles are equal and consecutive angles are supplementary.

Statement One Alone:
y = 2x

Since y and x are consecutive angles, they are supplementary (i.e., add up to 180 degrees). That is,

x + y = 180

Since y = 2x, we have:

x + 2x = 180

3x = 180

x = 60

Statement one alone is sufficient.

Statement Two Alone:
x + z = 120

Since x and z are opposite angles, they are equal in measure. That is,

x = z

Since x + z = 120, we have:

x + x = 120

2x = 120

x = 60

Statement two alone is sufficient.

Answer: D
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In a parallelogram,
adjacent angles sun to 180, and opp angles are equal.

Thats all you need to solve for this.

Each of these properties helps to solve using each of the given in the question stem.

Hence, D -> each statement is individually adequate.

Answer: Option D

Video solution by GMATinsight



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For quadrilateral angles, the formula for sum of angles <angle = 180x(n-2).
Since, figure is ||gm, opposite angles are equal.
1. As, y = 2x. using sum formula, x can be calculated. (Sufficient)
2. As, x+z=120. x and z are opposite and same, x can be calculated. (Sufficient)
Ans D.