Given Pqrs Solve For X

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In the figure above, if PQRS is a parallelogram, then y - ten [#permalink] fifteen Oct 2012, 03:25

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PQRS.png [ x.9 KiB | Viewed 53620 times ]

In the figure in a higher place, if PQRS is a parallelogram, and so y - x =

(A) xxx
(B) 35
(C) 40
(D) 70
(Due east) 100

Practice Questions
Question: 62
Folio: 160
Difficulty: 650

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Posts: 87006

Re: In the figure above, if PQRS is a parallelogram, and then y - ten [#permalink] 15 Oct 2012, 03:25

In the effigy to a higher place, if PQRS is a parallelogram, then y - x =

(A) 30
(B) 35
(C) 40
(D) 70
(Due east) 100

In parallelogram corresponding angles are equal and consecutive angles are supplementary (supplementary angles are ii angles that add upwards to 180°), thus:

\(140=2y\) --> \(y=lxx\);
\(2y+10=180\) --> \(140+x=180\) --> \(10=40\);

Therefore, \(y-x=70-40=30\).

Answer: A.

For more than check Polygons chapter of Math Book: math-polygons-87336.html
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Re: In the figure higher up, if PQRS is a parallelogram, and so y - x [#permalink] fifteen Oct 2012, 03:34

[quote="Bunuel"] 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 - 10 =
(A) 30
(B) 35
(C) 40
(D) 70
(East) 100

Notation:- 1) Whatever two continuous interior angles of a parallelogram are supplementary.
2) Opposite angles are equal.

x= 180 - 140 = forty
x+2y = 180---> 2y = 180- 10 -----> 2y = 180- 40---->
y = 70

Thus y - ten = 70 - 40 = thirty
Reply A

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Re: In the effigy above, if PQRS is a parallelogram, then y - ten [#permalink] 15 Oct 2012, 10:08

In the effigy shown, bending x= QRS = QPS (opposite angles in parallelogram)
Also, intersecting lines PQ and PS, therefore QPS +Outerangle = 180
=> QPS =180-140 = forty
hence x =forty

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

Therefore, y-x =70-forty = xxx

Ans A.

Bunuel wrote:

The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Projection

Attachment:

PQRS.png

In the figure above, if PQRS is a parallelogram, then y - 10 =

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

Practice Questions
Question: 62
Page: 160
Difficulty: 650

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Re: In the effigy above, if PQRS is a parallelogram, then y - x [#permalink] 16 Oct 2012, 02:30

since contrary sides and angles in a parallelogram are equal we know that

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

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

so X=40

at present 2 means to go on sum of angles in parellogram is 360

and then we have 2X+4Y=360
4Y = 360-fourscore ( 40*2)
4Y=280
Y=70 therefore Y-X=70-40 = 30 Reply Choice A

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

In both cases Answer Option is A

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Re: In the effigy in a higher place, if PQRS is a parallelogram, then y - x [#permalink] 02 May 2013, 09:59

180-140= 40, x=forty
140/2y= seventy=y
y-x =
70-40=xxx

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Re: In the figure above, if PQRS is a parallelogram, then y - 10 [#permalink] 03 Jun 2016, 05:41

Bunuel wrote:

Attachment:

PQRS.png

In the effigy higher up, if PQRS is a parallelogram, and so y - 10 =

(A) 30
(B) 35
(C) forty
(D) 70
(East) 100

To solve nosotros need to review some rules most parallelograms.

In parallelograms there are two chief rules most the relationships betwixt the angles:

one) Opposite angles are equal

Thus, angle P = bending R, and Angle Q = Bending Southward.

2) Sequent 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 Southward, angles South and R, and angles R and Q.

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

Nosotros start by determining the value for angle P. We come across that angle P is part of a direct angle. Since the outside bending of angle P = 140 degrees, angle P must equal 40 degrees (since the ii angles must sum to 180 degrees).

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

Using our 2d rule of parallelograms, nosotros know that angles R and South must add together up to 180 degrees considering they are consecutive angles. Nosotros annotation that angle Due south is equal to 2y. Thus:

2y + x = 180

2y + 40 = 180

2y = 140

y = seventy

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

The answer is A.
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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink] 05 Jul 2017, 20:27

Answer is A

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In the figure above, if PQRS is a parallelogram, then y - x [#permalink] Updated on: 28 Oct 2021, xiv:35

Bunuel wrote:

Attachment:

PQRS.png

In the effigy 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'southward ane approach;

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

And then, ∠QPS = xl°

Side by side, since the PQ||RS, we know that the two circled angles are respective angles, which means those two angles are equal

If 2y° = 140°, and so we know that y = 70°

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

And then, 10 = twoscore°

This means y - x = lxx - twoscore = thirty

Answer: A

Thank you,
Brent
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Re: In the figure above, if PQRS is a parallelogram, then y - x [#permalink] 16 Aug 2022, 10:55

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Re: In the effigy to a higher place, if PQRS is a parallelogram, then y - x [#permalink]

16 Aug 2022, ten:55

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