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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] New post 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] New post 04 Aug 2008, 08:25
In the quadilateral
(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] New post 04 Aug 2008, 08:33
The answer is C.

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] New post 04 Aug 2008, 22:06
OA is C. thanks everyone
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Re: Geometry: Lines [#permalink] New post 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


Answer is C)

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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