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

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

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New post 08 Aug 2017, 10:57
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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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New post 08 Aug 2017, 12:00
Bunuel wrote:
Image
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 \(\triangle\) \(DBE\),

\(70 + r + s = 180\)

\(r + s = 180 - 70 => 110\)

\(r + s + u + v = 110 + 110 = 220\)

Answer (D)...

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

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New post 08 Aug 2017, 23:40
Image

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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New post 09 Aug 2017, 07:12
Bunuel wrote:
Image
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

Answer D

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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