Bunuel wrote:
In the figure above, two lines intersect. Which of the following must be equal to 180 – x?
(A) x + y
(B) x + z
(C) y + z
(D) y + w
(E) z + w
We see that 2x + y + z + w = 360. Dividing both sides by 2, we have:
x + (y + z + w)/2 = 180
(y + z + w)/2 = 180 - x
We see that (180 - x) equals (y + z + w)/2; however, this is not given in the choices. Upon further analysis, we see that w = y and z = 2x, so we have:
180 - x = (y + z + w)/2 = (y + 2x + y)/2 = x + y. Thus, we see that (180 - x) = x + y.
Alternate Solution:
From the figure, we observe that 2x + y = 180. Subtracting x from each side, we get x + y = 180 - x.
Answer: A
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