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What is the value of x + y in the figure above?

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What is the value of x + y in the figure above?  [#permalink]

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New post 26 Dec 2012, 05:18
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What is the value of x + y in the figure above?

(1) w= 95
(2) z = 125

Attachment:
Angles.png
Angles.png [ 8.38 KiB | Viewed 29884 times ]
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New post 26 Dec 2012, 05:23
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What is the value of x + y in the figure above?

Sum of Interior Angles of a polygon is \(180(n-2)\) where \(n\) is the number of sides (so is the number of angles). So, the sum of the interior angles of a quadrilateral is 180*2=360. Look at the diagram below:

Image

According to the above: (180-x)+(180-y)+(180-z)+(180-w)=360 --> x+y=360-w-z, so all we need to know is the values of w and z.

(1) w= 95. Not sufficient.
(2) z = 125. Not sufficient.

(1)+(2) Sufficient.

Answer: C.

Attachment:
Angles2.png
Angles2.png [ 9.97 KiB | Viewed 25860 times ]

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Re: What is the value of x + y in the figure above?  [#permalink]

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New post 13 Feb 2016, 13:15
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In line to Bunuel's solution, we can also solve it using exterior angle and vertical angle properties. The sum of all exterior angles for a polygon is 360. So x+y = 360 - (w+z), and both 1 and 2 together provide the same.
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What is the value of x + y in the figure above?  [#permalink]

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New post Updated on: 16 Apr 2018, 12:38
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Walkabout wrote:
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What is the value of x + y in the figure above?

(1) w= 95
(2) z = 125

Attachment:
Angles.png


Target question: What is the value of x + y?

Statement 1: w = 95

Important: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or length into having just one value. This concept is discussed in much greater detail in the second video below.

If w = 95, then the angle inside the quadrilateral must be 85.
Image
So, those 2 angles (95 and 85) are "locked." In other words, the 2 lines that create those two angles are locked in place to create the 95- and 85-degree angles.
However, line1 is not locked into place, so we can still move it, which means we can freely alter the size of angle y.
As such, the value of x + y will vary.
Since we cannot answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: z = 125
If z = 125, then the angle inside the quadrilateral must be 55.
Image
Since line2 is not locked into place, we can still move it, which means we can freely alter the size of angle x.
As such, the value of x + y will vary.
Since we cannot answer the target question with certainty, statement 2 is SUFFICIENT

Statements 1 and 2 combined:
We now have the following:
Image
Since all angles in a quadrilateral add to 360 degrees, we know that 85 + 55 + j + k = 360
If we solve for j + k, we get: j + k = 220

Also notice that, since angles x and k are on a line, it must be true that x + k = 180.
Similarly, it must be true that y + j = 180
If we combine both of these equations, we get: x + y + j + k = 360
Since we already know that j + k = 220, we can replace j + k with 220, to get:
x + y + 220 = 360
This means x + y = 140
Since we cannot answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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Originally posted by GMATPrepNow on 01 Sep 2017, 15:09.
Last edited by GMATPrepNow on 16 Apr 2018, 12:38, edited 2 times in total.
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What is the value of x + y in the figure above?  [#permalink]

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New post 11 Nov 2017, 09:17
Bunuel wrote:
What is the value of x + y in the figure above?

Sum of Interior Angles of a polygon is \(180(n-2)\) where \(n\) is the number of sides (so is the number of angles). So, the sum of the interior angles of a quadrilateral is 180*2=360. Look at the diagram below:
Attachment:
Angles2.png
According to the above: (180-x)+(180-y)+(180-z)+(180-w)=360 --> x+y=360-w-z, so all we need to know is the values of w and z.

(1) w= 95. Not sufficient.
(2) z = 125. Not sufficient.

(1)+(2) Sufficient.

Answer: C.


If (180-w) = a and (180-z) = b, then the below generalized form is always true for any quadrilateral:
a+b=x+y

Maybe we can call it exterior angle theorem for quadrilaterals.
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What is the value of x + y in the figure above?  [#permalink]

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New post 07 Feb 2018, 06:31
Bunuel wrote:

Sum of Interior Angles of a polygon is \(180(n-2)\) where \(n\) is the number of sides (so is the number of angles). So, the sum of the interior angles of a quadrilateral is 180*2=360. Look at the diagram below:
Attachment:
Angles2.png
According to the above: (180-x)+(180-y)+(180-z)+(180-w)=360 --> x+y=360-w-z, so all we need to know is the values of w and z.

(1) w= 95. Not sufficient.
(2) z = 125. Not sufficient.

(1)+(2) Sufficient.

Answer: C.


How did you get from (180-x)+(180-y)+(180-z)+(180-w)=360 to x+y=360-w-z?

I am getting the following:

(180-z)+(180-w)=-180+x-180+y+360
-z-w=x+y+360
x+y=-360-z-w

Can you show more detail? Thanks in advance
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Re: What is the value of x + y in the figure above?  [#permalink]

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New post 07 Feb 2018, 06:51
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bpdulog wrote:
Bunuel wrote:

Sum of Interior Angles of a polygon is \(180(n-2)\) where \(n\) is the number of sides (so is the number of angles). So, the sum of the interior angles of a quadrilateral is 180*2=360. Look at the diagram below:
Attachment:
Angles2.png
According to the above: (180-x)+(180-y)+(180-z)+(180-w)=360 --> x+y=360-w-z, so all we need to know is the values of w and z.

(1) w= 95. Not sufficient.
(2) z = 125. Not sufficient.

(1)+(2) Sufficient.

Answer: C.


How did you get from (180-x)+(180-y)+(180-z)+(180-w)=360 to x+y=360-w-z?

I am getting the following:

(180-z)+(180-w)=-180+x-180+y+360
-z-w=x+y+360
x+y=-360-z-w

Can you show more detail? Thanks in advance


\((180-x)+(180-y)+(180-z)+(180-w)=360\)

\(720 - x - y - z - w = 360\)

\(360 - x - y - z - w=0\)

\(360-w-z=x+y\)
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Re: What is the value of x + y in the figure above? (1) w = 95  [#permalink]

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Re: What is the value of x + y in the figure above? (1) w = 95   [#permalink] 19 Sep 2019, 02:27
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