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

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In the figure above, what is the sum of the nine angles labeled with [#permalink]

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New post 10 Jan 2016, 08:41
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A
B
C
D
E

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  35% (medium)

Question Stats:

66% (01:21) correct 34% (01:25) wrong based on 113 sessions

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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.

Attachment:
2016-01-10_1940.png
2016-01-10_1940.png [ 5.12 KiB | Viewed 1530 times ]

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Re: In the figure above, what is the sum of the nine angles labeled with [#permalink]

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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]

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New post 10 Jan 2016, 08:48
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Bunuel wrote:
Image
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.

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]

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New post 25 Jun 2016, 01:11
Bunuel wrote:
Image
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.

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]

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New post 25 Jun 2016, 02:19
3
bimalr9 wrote:
Bunuel wrote:
Image
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.

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 1206 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]

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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]

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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
In the figure above, what is the sum of the nine angles labeled with   [#permalink] 01 Mar 2017, 06:33
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