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# In the figure above, what is the value of c in terms of a and b?

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Joined: 02 Sep 2009
Posts: 55271
In the figure above, what is the value of c in terms of a and b?  [#permalink]

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05 Sep 2017, 23:50
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Difficulty:

35% (medium)

Question Stats:

85% (02:23) correct 15% (01:12) wrong based on 35 sessions

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In the figure above, what is the value of c in terms of a and b?

(A) a + 3b – 180
(B) 2a + 2b – 180
(C) 180 – a – b
(D) 360 – a – b
(E) 360 – 2a – 3b

Attachment:

2017-09-06_1035.png [ 8.73 KiB | Viewed 2238 times ]

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Re: In the figure above, what is the value of c in terms of a and b?  [#permalink]

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06 Sep 2017, 00:24
Bunuel wrote:

In the figure above, what is the value of c in terms of a and b?

(A) a + 3b – 180
(B) 2a + 2b – 180
(C) 180 – a – b
(D) 360 – a – b
(E) 360 – 2a – 3b

Attachment:
2017-09-06_1035.png

180-(a+b) + 180-(a+b) + 180-(c+b) = 180
360 -2a-3b - c = 0
c = 360-2a-3b

E
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In the figure above, what is the value of c in terms of a and b?  [#permalink]

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06 Sep 2017, 00:28
Solution in attached figure:

Concept used: Sum of all angles in triangle =180
Sum of all angles on a straight line = supplementary = 180

x= 180-a-b
y=180-a-b
z=180-b-c

x+y+z =180
180-a-b + 180-a-b + 180-b-c = 180
360-2a-3b-c = 0
c = 360-2a-3b

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In the figure above, what is the value of c in terms of a and b?  [#permalink]

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06 Sep 2017, 07:44
1
Bunuel wrote:

In the figure above, what is the value of c in terms of a and b?

(A) a + 3b – 180
(B) 2a + 2b – 180
(C) 180 – a – b
(D) 360 – a – b
(E) 360 – 2a – 3b

Attachment:
2017-09-06_1035.png

Ignore the rightmost triangle with no variables given for its angle measures.

The sum of interior angles of a quadrilateral is 360 degrees.

[Sum of a polygon's interior angles is (n - 2) * 180, where n is the number of sides of the polygon.]

3b + 2a + c = 360

c = 360 - 2a - 3b

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In the figure above, what is the value of c in terms of a and b?   [#permalink] 06 Sep 2017, 07:44
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