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

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

[Reveal] Spoiler:
Attachment:
Angles.png
Angles.png [ 8.38 KiB | Viewed 12623 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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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
Angles2.png [ 9.97 KiB | Viewed 11648 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.

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

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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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Walkabout wrote:
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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.
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:
[Reveal] Spoiler:
C


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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] 11 Nov 2017, 09:17
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