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In the figure above, what is the sum of the nine angles labeled with

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Bunuel
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In the figure above, what is the sum of the nine angles labeled with [#permalink] New post   10 Jan 2016, 08:41
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In the figure above, what is the sum of the nine angles labeled with letters?

A. 138°
B. 378°
C. 678°
D. 900°
E. It cannot be determined from the information given.

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D
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thac
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Re: In the figure above, what is the sum of the nine angles labeled with [#permalink] New post   10 Jan 2016, 08:47
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Wouldn't it be 900°?

There's 180° total in the triangle. If we assume that all 4 corners of each side of the triangle form a circle, that would be 360° * 3 = 1080°

1080° - 180° from the angles not labeled inside the triangle = 900°

Ans D

Please let me know if there are any mistakes here
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Re: In the figure above, what is the sum of the nine angles labeled with [#permalink] New post   10 Jan 2016, 08:48
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Bunuel wrote:

In the figure above, what is the sum of the nine angles labeled with letters?

A. 138°
B. 378°
C. 678°
D. 900°
E. It cannot be determined from the information given.

Show Spoiler
Attachment:
2016-01-10_1940.png


Answer D

Question
a+b+c+d+e+f+g+h+i =?

a+b+c = 360-42 = 318
g+h= 180 (On Straight Line)
e+f = 180 (On Straight line)

Considering triangle
180-d+180-i+42= 180
d+i= 222

So a+b+c+d+e+f+g+h+i= 318+180+180+222=900
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In the figure above, what is the sum of the nine angles labeled with [#permalink] New post   25 Jun 2016, 01:11
Bunuel wrote:

In the figure above, what is the sum of the nine angles labeled with letters?

A. 138°
B. 378°
C. 678°
D. 900°
E. It cannot be determined from the information given.

Show Spoiler
Attachment:
2016-01-10_1940.png


Abhishek009 VeritasPrepKarishma Skywalker18 Engr2012 is the method of thac correct.
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Re: In the figure above, what is the sum of the nine angles labeled with [#permalink] New post   25 Jun 2016, 02:19
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bimalr9 wrote:
Bunuel wrote:

In the figure above, what is the sum of the nine angles labeled with letters?

A. 138°
B. 378°
C. 678°
D. 900°
E. It cannot be determined from the information given.

Show Spoiler
Attachment:
The attachment 2016-01-10_1940.png is no longer available


Abhishek009 VeritasPrepKarishma Skywalker18 Engr2012 is the method of thac correct.


IMHO no issues with that way of solving this problem and consider it to be a very very elegant way of solving the problem in least amount of time....

Consider the case here -

Attachment:
2016-01-10_1940.png
2016-01-10_1940.png [ 7.27 KiB | Viewed 4079 times ]


In the triangle -

42 + m + n = 180

So, m + n = 138

No go for solving the circles

(a+b+c+42) = ( m + d + e + f ) = (n + g + h + i ) = 360

Add those -

(a+b+c+42) + ( m + d + e + f ) + (n + g + h + i ) = 360 + 360 + 360

a+b+c+42 +m + d + e + f + n + g + h + i = 1080

a+ b + c + ( m + n ) + d + e + f + g + h + i = 1038

a+ b + c + 138 + d + e + f + g + h + i = 1038

a+ b + c + d + e + f + g + h + i = 900

Hence answer will be (D)

Hope this helps.....
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Re: In the figure above, what is the sum of the nine angles labeled with [#permalink] New post   28 Sep 2016, 06:33
a + b = 180
d + e = 180
h + i = 180
c +42 = 180

(180-f) + (180-g)+42 = 180
f+g -42= 180

Add above equation

a+b+c+d+e+f+g+h+i = 180 * 5 = 900 Ans D.
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In the figure above, what is the sum of the nine angles labeled with [#permalink] New post   01 Mar 2017, 06:33
Sum of angles at each edge = 360*3 = 1080
Sum of interior angles of triangle = 180
Sum of rest of the angles = 1080-180=900. Option D
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Re: In the figure above, what is the sum of the nine angles labeled with [#permalink] New post   10 Mar 2023, 22:14
Angles in a straight line = 180.
Opposite angles are equal.
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Re: In the figure above, what is the sum of the nine angles labeled with [#permalink]
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