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# In the figure above, if m is parallel to n, which of the following is

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Math Expert
Joined: 02 Sep 2009
Posts: 54376
In the figure above, if m is parallel to n, which of the following is  [#permalink]

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01 Aug 2017, 04:54
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35% (medium)

Question Stats:

65% (01:28) correct 35% (01:39) wrong based on 22 sessions

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In the figure above, if m is parallel to n, which of the following is true?

(A) x + z = 90 + y
(B) z = x – y
(C) x + y + z = 180
(D) y = z + x
(E) x = z – y

Attachment:

2017-08-01_1349_002.png [ 4.55 KiB | Viewed 912 times ]

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In the figure above, if m is parallel to n, which of the following is  [#permalink]

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01 Aug 2017, 05:29
If you extend the line from m to n, it forms a triangle.

The first angle of the triangle is z.
Since, sum of angles in a straight line is 180 degree, the second angle of the triangle is 180-y
The angle on the line n would be 180 - x because the alternate interior angles are supplementary.
Since, sum of angles in a straight line is 180 degree, the third angle of the triangle is x

The angles of the triangle is z,x and 180-y.
Since the sum of the angles in a triangle is 180 degree,
z + x + 180 - y = 180
z + x = y(Option D)
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Re: In the figure above, if m is parallel to n, which of the following is  [#permalink]

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02 Aug 2017, 13:30
Bunuel wrote:

In the figure above, if m is parallel to n, which of the following is true?

(A) x + z = 90 + y
(B) z = x – y
(C) x + y + z = 180
(D) y = z + x
(E) x = z – y

Attachment:
2017-08-01_1349_002.png

We can draw a line (let’s call it line p) through the vertex of angle y such that line p is parallel to both lines m and n. We will see that angle y is split into two angles such that the upper one is equal in measure to angle x, since they are alternate interior angles of two parallel lines cut by a transversal, and the lower one is equal in measure to angle z for the same reason. Thus, y = x + z.

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Re: In the figure above, if m is parallel to n, which of the following is   [#permalink] 02 Aug 2017, 13:30
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