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In the figure above, what is the value of a + b + c?

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Bunuel
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In the figure above, what is the value of a + b + c? [#permalink] New post   15 Aug 2017, 02:19
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In the figure above, what is the value of a + b + c?

(A) 300
(B) 330
(C) 360
(D) 400
(E) 450

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Re: In the figure above, what is the value of a + b + c? [#permalink] New post   15 Aug 2017, 03:24
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Let the internal angles of the triangle be x, y & z

(x + a) = 180 --- 1
(y + b) = 180 --- 2
(z + c) = 180 --- 3
Adding all 3 equations :
x + y + z + a + b + c = 540

Since x + y + z = 180 :

a + b + c = 540 - 180 = 360 --> Option (C)
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In the figure above, what is the value of a + b + c? [#permalink] New post   15 Aug 2017, 02:52
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The sum of an interior angle and exterior angle pair is always 180 degrees.

Since there are 3 such pairs the sum must be 540 degree.
But the sum of the angles in a triangle(each of the interior angles) is always 180 degree.

Therefore, sum of the exterior angles a,b, and c is 540 - 180 = 360(Option C)
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Re: In the figure above, what is the value of a + b + c? [#permalink] New post   15 Aug 2017, 02:48
will go with 360 ...
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
following this property we will get = 2(180) = a+b+c = 360.
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Re: In the figure above, what is the value of a + b + c? [#permalink] New post   15 Aug 2017, 03:40
180-a + 180-b + 180-c= 180
540-(a+b+c)=180
a+b+c=360
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In the figure above, what is the value of a + b + c? [#permalink] New post   15 Aug 2017, 18:58
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Bunuel wrote:

In the figure above, what is the value of a + b + c?

(A) 300
(B) 330
(C) 360
(D) 400
(E) 450

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Attachment:
2017-08-15_1312_002.png

No calculation required.

The sum of the exterior angles of any convex polygon is 360°.

Angles a, b, and c are exterior angles.* Their sum is 360°.

Answer C


*In the diagram, b and c are successive exterior angles (starting at b, moving clockwise). If you continue to move clockwise, strictly speaking, you would come to the angle opposite from a -- which is a vertical angle that equals a. Likewise, you could start at a, go counterclockwise, and do the same for b and c (opposite vertical angles are congruent).
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Re: In the figure above, what is the value of a + b + c? [#permalink] New post   15 Aug 2017, 19:30
3 sets of angles each 360 = so total 1080
(1080 - 180*2)/2 360
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Re: In the figure above, what is the value of a + b + c? [#permalink] New post   18 Aug 2017, 09:10
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Bunuel wrote:

In the figure above, what is the value of a + b + c?

(A) 300
(B) 330
(C) 360
(D) 400
(E) 450


We see that a + b + c is the sum of the exterior angles of the triangle. Since the sum of the exterior angles of any polygon is equal to 360, a + b + c = 360.

Answer: C
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Re: In the figure above, what is the value of a + b + c? [#permalink] New post   26 Oct 2023, 09:21
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Re: In the figure above, what is the value of a + b + c? [#permalink]
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