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# In the figure above, two lines intersect. Which of the following must

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Math Expert
Joined: 02 Sep 2009
Posts: 58421
In the figure above, two lines intersect. Which of the following must  [#permalink]

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19 Jul 2017, 03:53
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35% (medium)

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73% (01:44) correct 27% (02:01) wrong based on 56 sessions

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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

Attachment:

2017-07-19_1452.png [ 5.48 KiB | Viewed 911 times ]

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Re: In the figure above, two lines intersect. Which of the following must  [#permalink]

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19 Jul 2017, 04:13
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

Attachment:
2017-07-19_1452.png

It should be A

A - $$y + 2x = 180$$ --> $$y + x + x = 180$$ --> $$180 - x = x + y$$
B - information doesn't suggest this is the case.
C - y + z = 180
D - information doesn't suggest this is the case.
E - z + w = 180
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Re: In the figure above, two lines intersect. Which of the following must  [#permalink]

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19 Jul 2017, 04:23
y=180-2x
z=2x
w=y=180-2x

Now if i chose

option A which is x+y = x+180-2x = 180-x
option B which is x+z =x+2x= 3x
option C which is y+z = 180-2x+2x= 180
option D which is y+w = 180-2x+180-2x= 360-4x
Option E which is z+w = 2x+180-2x=180

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Re: In the figure above, two lines intersect. Which of the following must  [#permalink]

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25 Jul 2017, 10:56
1
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.

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Re: In the figure above, two lines intersect. Which of the following must  [#permalink]

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28 Feb 2019, 10:50
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Re: In the figure above, two lines intersect. Which of the following must   [#permalink] 28 Feb 2019, 10:50
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# In the figure above, two lines intersect. Which of the following must

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