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In the figure above, n is perpendicular to m, and p is parallel to q.

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In the figure above, n is perpendicular to m, and p is parallel to q. [#permalink]

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New post 08 Aug 2017, 01:58
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In the figure above, n is perpendicular to m, and p is parallel to q. What is the value of x + y + z?

(A) 180
(B) 220
(C) 230
(D) 270
(E) 310


[Reveal] Spoiler:
Attachment:
2017-08-08_1257.png
2017-08-08_1257.png [ 7.16 KiB | Viewed 510 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, n is perpendicular to m, and p is parallel to q. [#permalink]

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New post 08 Aug 2017, 02:13
Bunuel wrote:
Image
In the figure above, n is perpendicular to m, and p is parallel to q. What is the value of x + y + z?

(A) 180
(B) 220
(C) 230
(D) 270
(E) 310


[Reveal] Spoiler:
Attachment:
2017-08-08_1257.png


It should be D

x:
\(\angle 110\) and \(\angle x\) are opposite angles so this makes \(\angle x = 110\)

y:
\(\angle y = 90 = 180\) which means
\(\angle y = 90\)

z:

\(\angle x + \angle z = 180\)
we already know \(\angle x = 110\)
This makes
\(\angle z = 70\)

\(\angle x + \angle y + \angle z = 110 + 90 + 70 = 270\)
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Re: In the figure above, n is perpendicular to m, and p is parallel to q. [#permalink]

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New post 10 Aug 2017, 11:29
Bunuel wrote:
Image
In the figure above, n is perpendicular to m, and p is parallel to q. What is the value of x + y + z?

(A) 180
(B) 220
(C) 230
(D) 270
(E) 310


[Reveal] Spoiler:
Attachment:
2017-08-08_1257.png


We see that x is opposite the 110 degree angle, so x = 110 as well. Angle y is supplementary with a 90 degree angle, so y = 90. Since lines q and p are parallel, z = 180 - 110 = 70.

Thus, x + y + z = 270.

Answer: D
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Re: In the figure above, n is perpendicular to m, and p is parallel to q.   [#permalink] 10 Aug 2017, 11:29
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In the figure above, n is perpendicular to m, and p is parallel to q.

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