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

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Math Expert
Joined: 02 Sep 2009
Posts: 47088
In the figure above, n is perpendicular to m, and p is parallel to q. [#permalink]

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08 Aug 2017, 01:58
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Difficulty:

25% (medium)

Question Stats:

100% (00:36) correct 0% (00:00) wrong based on 26 sessions

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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

Attachment:

2017-08-08_1257.png [ 7.16 KiB | Viewed 688 times ]

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Joined: 14 Oct 2015
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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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08 Aug 2017, 02:13
Bunuel wrote:

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

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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10 Aug 2017, 11:29
Bunuel wrote:

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

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.

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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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