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

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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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Difficulty:

25% (medium)

Question Stats:

90% (00:35) correct 10% (01:34) wrong based on 31 sessions

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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

Attachment:

2017-08-08_2137.png [ 6.93 KiB | Viewed 845 times ]

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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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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

Attachment:
2017-08-08_2137.png

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

$$70 + u + v = 180$$

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

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

$$70 + r + s = 180$$

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

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

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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)
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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

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

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

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