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# In the figure, x + y =

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Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128870 [0], given: 12183

In the figure, x + y = [#permalink]

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20 Sep 2017, 22:49
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In the figure, x + y =

(A) 60
(B) 135
(C) 165
(D) 195
(E) 220

[Reveal] Spoiler:
Attachment:

2017-09-20_1021_001.png [ 7.71 KiB | Viewed 376 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 128870 [0], given: 12183

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 1454

Kudos [?]: 594 [0], given: 16

Location: India
WE: Sales (Retail)
Re: In the figure, x + y = [#permalink]

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21 Sep 2017, 00:41

The four lines form a quadrilateral
The two angles that lie of the same straight line as the angles given(135 and 60)
are $$180 - 135 = 45$$ and $$180 - 60 = 120$$ respectively.
The other two angles in the quadrilateral are 180 - x and 180 - y

The sum of the angles in a quadrilateral is 360 degree.

180 - x + 180 - y + 120 + 45 = 360
x+y = 165 degree(Option C)
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Kudos [?]: 594 [0], given: 16

Manager
Joined: 25 Nov 2015
Posts: 228

Kudos [?]: 64 [0], given: 239

Location: India
GPA: 3.64
WE: Engineering (Energy and Utilities)
Re: In the figure, x + y = [#permalink]

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21 Sep 2017, 10:33
In the given quadrilateral, sum of interior angles =180(n-2)=180x2=360
Sum of interior angles are (180-x)+(180-y)+(180-135)+(180-60)
=(180-x)+(180-y)+45+120=360
x+y=165
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Kudos [?]: 64 [0], given: 239

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1634

Kudos [?]: 838 [1], given: 2

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Re: In the figure, x + y = [#permalink]

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25 Sep 2017, 16:35
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Expert's post
Bunuel wrote:

In the figure, x + y =

(A) 60
(B) 135
(C) 165
(D) 195
(E) 220

Since the exterior angles of any polygon must sum to 360 degrees, we have:

x + y + 60 + 135 = 360

x + y = 165

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Kudos [?]: 838 [1], given: 2

Re: In the figure, x + y =   [#permalink] 25 Sep 2017, 16:35
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