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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
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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:
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Angles2.png [ 9.97 KiB | Viewed 7217 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
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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.
Re: What is the value of x + y in the figure above?   [#permalink] 13 Feb 2016, 13:15
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