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

Question

https://gmatclub.com/forum/download/file.php?id=28903 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. 2016-01-10_1940.png

thac · Answer

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

Praveengeol · Answer

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

bimalr9 · Answer

Abhishek009   VeritasPrepKarishma   Skywalker18   Engr2012  is the method of  thac  correct.

Abhishek009 · Answer

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 - 2016-01-10_1940.png 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.....

0ld · Answer

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.

KrishnakumarKA1 · Answer

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

adityasuresh · Answer

Angles in a straight line = 180.
Opposite angles are equal.

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

Prep Toolkit

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