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# In the figure above, n is parallel to p. If x = 30 and y = 80, what is

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Joined: 02 Sep 2009
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In the figure above, n is parallel to p. If x = 30 and y = 80, what is  [#permalink]

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01 Aug 2017, 05:04
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Question Stats:

95% (01:07) correct 5% (00:49) wrong based on 56 sessions

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In the figure above, n is parallel to p. If x = 30 and y = 80, what is the value of z?

(A) 70
(B) 65
(C) 60
(D) 55
(E) 50

Attachment:

2017-08-01_1350_003.png [ 10.05 KiB | Viewed 994 times ]

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Re: In the figure above, n is parallel to p. If x = 30 and y = 80, what is  [#permalink]

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01 Aug 2017, 07:16
Quote:

Given data: x=30, y=80.

We have been asked to find the value of z.

In the triangle formed,
the angles formed are x(adjacent angles), y(corresponding angles because n || p) and z.

We know the sum of angles in a triangle is 180 degree.
x + y + z = 180
Substituting values, 30 + 80 + z = 180 or z = 70 (Option A)
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Re: In the figure above, n is parallel to p. If x = 30 and y = 80, what is  [#permalink]

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01 Aug 2017, 07:55
Bunuel wrote:

In the figure above, n is parallel to p. If x = 30 and y = 80, what is the value of z?

(A) 70
(B) 65
(C) 60
(D) 55
(E) 50

Attachment:
The attachment 2017-08-01_1350_003.png is no longer available

Parallel lines makes same angle on a 3rd line.
Attachment:

IMG_20170801_202416.jpg [ 106.27 KiB | Viewed 753 times ]

hence option A
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Re: In the figure above, n is parallel to p. If x = 30 and y = 80, what is  [#permalink]

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02 Aug 2017, 13:32
Bunuel wrote:

In the figure above, n is parallel to p. If x = 30 and y = 80, what is the value of z?

(A) 70
(B) 65
(C) 60
(D) 55
(E) 50

Attachment:
2017-08-01_1350_003.png

We see that angle z is the vertical angle of (and thus equal to) one of the angles of the smaller triangle shown, angle y is the vertical angle of (and thus equal to) another angle of the smaller triangle, and angle x is the corresponding angle of (and thus equal to) the last angle of the smaller triangle. Thus, x + y + z = 180. Since x = 30 and y = 80, we have:

30 + 80 + z = 180

z = 70

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Re: In the figure above, n is parallel to p. If x = 30 and y = 80, what is  [#permalink]

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02 Aug 2017, 20:05

Much simpler method

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Re: In the figure above, n is parallel to p. If x = 30 and y = 80, what is   [#permalink] 02 Aug 2017, 20:05
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