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# In the figure above, p + q =

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Math Expert
Joined: 02 Sep 2009
Posts: 49303
In the figure above, p + q =  [#permalink]

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05 Oct 2017, 01:30
00:00

Difficulty:

25% (medium)

Question Stats:

66% (01:12) correct 34% (01:10) wrong based on 41 sessions

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In the figure above, p + q =

(A) 100
(B) 145
(C) 165
(D) 195
(E) 215

Attachment:

2017-10-04_1124_002.png [ 8.24 KiB | Viewed 674 times ]

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Joined: 09 Aug 2017
Posts: 4
Re: In the figure above, p + q =  [#permalink]

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05 Oct 2017, 01:32
The answer should be D since angle p and q are alternate angles.

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Senior Manager
Joined: 02 Jul 2017
Posts: 294
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
Re: In the figure above, p + q =  [#permalink]

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05 Oct 2017, 03:01
In the figure above, p + q =

* Here Lines are not parallel ( Nothing given about lines)

The center part of figure forms a quadrilateral. And sum of all angles of quadrilateral = (4-2)*180 = 360

Now find angles of quadrilateral = 80, (180-115) , (180-p) and (180-q)

=> 80+ 65 + 180-p+180-q = 360
=> p+q = 80+65 = 145

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Re: In the figure above, p + q =  [#permalink]

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05 Oct 2017, 03:03
themorningowl92 wrote:
The answer should be D since angle p and q are alternate angles.

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Here we cannot say that p and q are alternate angles as we don't know if lines are parallel or not.

Also if both pair of lines were supposed to be parallel, angles marked 115 and 80 will become equal, but that's not the case here.
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Re: In the figure above, p + q =  [#permalink]

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09 Oct 2017, 16:47
2
Bunuel wrote:

In the figure above, p + q =

(A) 100
(B) 145
(C) 165
(D) 195
(E) 215

Attachment:
2017-10-04_1124_002.png

Since the sum of all the exterior angles of a polygon is 360, we note that 115, p, and q are measures of three of the four exterior angles of the quadrilateral, while the last exterior angle measures 180 - 80 = 100 degrees. We can now set up the following equation:

115 + p + q + 100 = 360

215 + p + q = 360

p + q = 145

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Re: In the figure above, p + q = &nbs [#permalink] 09 Oct 2017, 16:47
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# In the figure above, p + q =

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