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# What is the value of x + y in the figure above? (1) w = 95

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What is the value of x + y in the figure above? (1) w = 95 [#permalink]  04 Aug 2008, 08:02
What is the value of x + y in the figure above?
(1) w = 95
(2) z = 125

Are there some rules that I'm missing here? Cause i really don't know where to go from the statements.
thanks
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Re: Geometry: Lines [#permalink]  04 Aug 2008, 08:25
(180-x)+ (180-y) +(180 -w) + (180-z) = 360

-->180 -x + 180-y + 55 + 85 = 360

--> x + y = 140

(C)
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Re: Geometry: Lines [#permalink]  04 Aug 2008, 08:33

If you think of the angles, like angle W + the angle to its right that together form the straight line, then 180 - W will be the interior angle. I called this $$W_1$$. If you think of the interior angle adjacent to each letter as that $$Z_1, Y_1, X_1$$, then you will have the following equation:

$$x + y = w_1 + z_1$$

When you know the values of w & z, then it allows you to do $$180-w = W_1$$ and $$180-z = Z_1$$

Then once you know those 2 interior angles, the other 2 angles (that are $$X_1$$ and $$Y_1$$ is equal to $$360 - W_1 - Z_1$$ So now you have $$X_1 + Y_1 = 360 - W_1 - Z_1$$

You also know that $$x + X_1 + y + Y_1 = 360$$ because each of those 4 angles add up to make 360. Each $$x & X_1$$ and $$y & Y_1$$ form a straight line which is 180 degrees. because there are 2, then it's 180 + 180.
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Re: Geometry: Lines [#permalink]  04 Aug 2008, 22:06
OA is C. thanks everyone
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Re: Geometry: Lines [#permalink]  04 Aug 2008, 22:45
tarek99 wrote:
What is the value of x + y in the figure above?
(1) w = 95
(2) z = 125

Are there some rules that I'm missing here? Cause i really don't know where to go from the statements.
thanks

Sum of internal angles of quad is 360

Therefore x+ y = 360 - (180 -95) - (180 - 125) = 360 -140 = 220
Re: Geometry: Lines   [#permalink] 04 Aug 2008, 22:45
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