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# In ∆ ABC above, what is the value of r + s + u + v?

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Math Expert
Joined: 02 Sep 2009
Posts: 41631

Kudos [?]: 124107 [0], given: 12071

In ∆ ABC above, what is the value of r + s + u + v? [#permalink]

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08 Aug 2017, 10:39
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In ∆ ABC above, what is the value of r + s + u + v?

(A) 180
(B) 200
(C) 210
(D) 220
(E) 230

[Reveal] Spoiler:
Attachment:

2017-08-08_2137.png [ 6.93 KiB | Viewed 425 times ]
[Reveal] Spoiler: OA

_________________

Kudos [?]: 124107 [0], given: 12071

BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 1321

Kudos [?]: 518 [0], given: 16

Location: India
WE: Sales (Retail)
In ∆ ABC above, what is the value of r + s + u + v? [#permalink]

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08 Aug 2017, 10:57

In ∆ABC, u+v+70 = 180
u+v = 110

Lets call the line in between DE
In ∆BDE, r+s+70 = 180
r+s = 110

r+s+u+v = 220(Option D)
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Kudos [?]: 518 [0], given: 16

Director
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 262 [0], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
In ∆ ABC above, what is the value of r + s + u + v? [#permalink]

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08 Aug 2017, 12:00
Bunuel wrote:

In ∆ ABC above, what is the value of r + s + u + v?

(A) 180
(B) 200
(C) 210
(D) 220
(E) 230

[Reveal] Spoiler:
Attachment:
2017-08-08_2137.png

In $$\triangle$$ $$ABC$$,

$$70 + u + v = 180$$

$$u + v = 180 - 70 => 110$$

Let the smaller triangle be $$\triangle$$ $$DBE$$,

$$70 + r + s = 180$$

$$r + s = 180 - 70 => 110$$

$$r + s + u + v = 110 + 110 = 220$$

Kudos [?]: 262 [0], given: 261

Manager
Joined: 23 Jul 2015
Posts: 148

Kudos [?]: 32 [0], given: 29

GMAT 1: 730 Q50 V40
Re: In ∆ ABC above, what is the value of r + s + u + v? [#permalink]

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08 Aug 2017, 23:40

Lets call intersecting line DE

Sum of interior angles in a triangle = 180

Here we have two triangles $$\triangle ABC$$ and $$\triangle BDE$$

70 + u + v + 70 + r + s = 360
therefore, u + v + r + s = 220 (choice D)

Kudos [?]: 32 [0], given: 29

Director
Joined: 22 May 2016
Posts: 624

Kudos [?]: 182 [0], given: 494

In ∆ ABC above, what is the value of r + s + u + v? [#permalink]

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09 Aug 2017, 07:12
Bunuel wrote:

In ∆ ABC above, what is the value of r + s + u + v?

(A) 180
(B) 200
(C) 210
(D) 220
(E) 230

[Reveal] Spoiler:
Attachment:
2017-08-08_2137.png

From smaller and larger triangles, then add:

r + s + 70 = 180
u + v + 70 = 180
--------------------------------
r + s + u + v + 140 = 360

r + s + u + v = 220

Kudos [?]: 182 [0], given: 494

In ∆ ABC above, what is the value of r + s + u + v?   [#permalink] 09 Aug 2017, 07:12
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