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# In the figure above, if PQRS is a parallelogram, then y - x

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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]
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In the figure shown, angle x= QRS = QPS (opposite angles in parallelogram)
Also, intersecting lines PQ and PS, therefore QPS +Outerangle = 180
=> QPS =180-140 = 40
hence x =40

Also, Lines PQ and RS are parallel so angles they make with horizontal line PS are same. hence 2y =140
=> y =70

Therefore, y-x =70-40 = 30

Ans A.

Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Attachment:
PQRS.png
In the figure above, if PQRS is a parallelogram, then y - x =

(A) 30
(B) 35
(C) 40
(D) 70
(E) 100

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Question: 62
Page: 160
Difficulty: 650

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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]
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since opposite sides and angles in a parallelogram are equal we know that

angle QRS = QPS = X
angle RSP = RPQ = 2y

140 + angle QPS = 180 ( sum of 2 angles on a straight line)

so X=40

now 2 ways to proceed sum of angles in parellogram is 360

so we have 2X+4Y=360
4Y = 360-80 ( 40*2)
4Y=280
Y=70 therefore Y-X=70-40 = 30 Answer Choice A

The other way since opposite sides are parallel PQ ll RS
hence 2Y=140 >>> y=70 and then Y-x = 70-40 = 30

In both cases Answer Choice is A
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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]
180-140= 40, x=40
140/2y= 70=y
y-x =
70-40=30
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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]
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Bunuel wrote:
Attachment:
PQRS.png
In the figure above, if PQRS is a parallelogram, then y - x =

(A) 30
(B) 35
(C) 40
(D) 70
(E) 100

To solve we need to review some rules about parallelograms.

In parallelograms there are two main rules about the relationships between the angles:

1) Opposite angles are equal

Thus, angle P = angle R, and Angle Q = Angle S.

2) Consecutive angles are supplementary. That is, they add to 180 degrees.

Thus, angles Q and P add up to 180 degrees, as do angles P and S, angles S and R, and angles R and Q.

These rules can be used to solve the problem at hand.

We start by determining the value for angle P. We see that angle P is part of a straight angle. Since the exterior angle of angle P = 140 degrees, angle P must equal 40 degrees (since the two angles must sum to 180 degrees).

Using our first rule of parallelograms we see that angle R, which is equal to x, must also measure 40 degrees, since angles P and R are opposite angles.

Using our second rule of parallelograms, we know that angles R and S must add up to 180 degrees because they are consecutive angles. We note that angle S is equal to 2y. Thus:

2y + x = 180

2y + 40 = 180

2y = 140

y = 70

Therefore, the value of y – x is 70 – 40 = 30.

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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]
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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]
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Bunuel wrote:
Attachment:
PQRS.png
In the figure above, if PQRS is a parallelogram, then y - x =

(A) 30
(B) 35
(C) 40
(D) 70
(E) 100

There are several ways to solve this question.
Here's one approach;

Since the two highlighted angles below share the same line, they must add to 180°

So, ∠QPS = 40°

Next, since the PQ||RS, we know that the two circled angles are corresponding angles, which means those two angles are equal

If 2y° = 140°, then we know that y = 70°

Finally, since the two angles (circled in blue below) are opposite angles in a parallelogram, we know that they are EQUAL.

So, x = 40°

This means y - x = 70 - 40 = 30

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 13 Sep 2017, 11:11.
Last edited by BrentGMATPrepNow on 28 Oct 2021, 15:35, edited 1 time in total.
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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]
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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink]
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