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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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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

[Reveal] Spoiler:
Attachment:

Angles.png [ 8.38 KiB | Viewed 11965 times ]
[Reveal] Spoiler: OA

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

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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:
Attachment:

Angles2.png [ 9.97 KiB | Viewed 11126 times ]
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.

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

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30 Jun 2014, 10:43
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Re: What is the value of x + y in the figure above? [#permalink]

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29 Jul 2015, 07:32
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Re: What is the value of x + y in the figure above? [#permalink]

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

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17 Apr 2017, 01:51
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Re: What is the value of x + y in the figure above? [#permalink]

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01 Sep 2017, 15:09
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What is the value of x + y in the figure above?

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

[Reveal] Spoiler:
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

[Reveal] Spoiler:
C

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Re: What is the value of x + y in the figure above?   [#permalink] 01 Sep 2017, 15:09
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