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

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Manager
Joined: 02 Dec 2012
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What is the value of x + y in the figure above?  [#permalink]

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26 Dec 2012, 04:18
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65% (01:27) correct 35% (01:20) wrong based on 1807 sessions

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

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

Attachment:

Angles.png [ 8.38 KiB | Viewed 21123 times ]
Math Expert
Joined: 02 Sep 2009
Posts: 50615
What is the value of x + y in the figure above?  [#permalink]

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26 Dec 2012, 04:23
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14

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:

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.

Attachment:

Angles2.png [ 9.97 KiB | Viewed 18414 times ]

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Manager
Joined: 12 Feb 2011
Posts: 88
Re: What is the value of x + y in the figure above?  [#permalink]

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13 Feb 2016, 12:15
2
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.
CEO
Joined: 11 Sep 2015
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What is the value of x + y in the figure above?  [#permalink]

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Updated on: 16 Apr 2018, 11:38
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Top Contributor

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.

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.

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:

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

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Originally posted by GMATPrepNow on 01 Sep 2017, 14:09.
Last edited by GMATPrepNow on 16 Apr 2018, 11:38, edited 2 times in total.
Intern
Joined: 16 Sep 2017
Posts: 3
What is the value of x + y in the figure above?  [#permalink]

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11 Nov 2017, 08:17
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.

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.
Manager
Joined: 14 Aug 2012
Posts: 83
GMAT 1: 620 Q43 V33
What is the value of x + y in the figure above?  [#permalink]

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07 Feb 2018, 05:31
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.

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

Math Expert
Joined: 02 Sep 2009
Posts: 50615
Re: What is the value of x + y in the figure above?  [#permalink]

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07 Feb 2018, 05:51
1
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.

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

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

$$720 - x - y - z - w = 360$$

$$360 - x - y - z - w=0$$

$$360-w-z=x+y$$
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Re: What is the value of x + y in the figure above? &nbs [#permalink] 07 Feb 2018, 05:51
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# What is the value of x + y in the figure above?

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