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In the figure above, p + q =

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

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New post 05 Oct 2017, 01:30
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (00:57) correct 37% (00:35) wrong based on 27 sessions

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In the figure above, p + q =

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

[Reveal] Spoiler:
Attachment:
2017-10-04_1124_002.png
2017-10-04_1124_002.png [ 8.24 KiB | Viewed 429 times ]
[Reveal] Spoiler: OA

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

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

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

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New post 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

Answer: B

Kudos [?]: 106 [0], given: 66

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

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New post 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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New post 09 Oct 2017, 16:47
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Expert's post
Bunuel wrote:
Image
In the figure above, p + q =

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

[Reveal] Spoiler:
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

Answer: B
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Kudos [?]: 1010 [1], given: 3

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