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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure, what is the value of a ? 09 Oct 2018, 01:45
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D
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Difficulty:

35% (medium)

Question Stats:

69% (01:59) correct 31% (02:04) wrong based on 52 sessions

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In the figure, what is the value of a ?

(A) 30
(B) 45
(C) 60
(D) 72
(E) 90


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lines (2).jpg [ 21.36 KiB | Viewed 7040 times ]
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D
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In the figure, what is the value of a ? 09 Oct 2018, 01:58
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Bunuel

In the figure, what is the value of a ?

(A) 30
(B) 45
(C) 60
(D) 72
(E) 90


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lines (2).jpg
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From the figure, we can find out that :

a °=2b ° & b °=3c ° ( vertically opposite angles are always equal )

Now, sum of total angles show in figure is 360 °

Therefore, a °+b °+6c °+2b °+3c °+6c °= 360 °
Solving this we get : a °+3b °+15c °=360 °

Now substitute, a °=2b ° & b °=3c °, we will get b°= 36°
Hence a°=2b°=2*36°= 72°. Option D is correct.
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In the figure, what is the value of a ? 09 Oct 2018, 02:24
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Ans is option D value is 72

AnupamKT ...plz note that nowhere it is mentioned about Vertical opposite angle in question....
Plz don't assume

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In the figure, what is the value of a ? 09 Oct 2018, 03:11
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Bunuel

In the figure, what is the value of a ?

(A) 30
(B) 45
(C) 60
(D) 72
(E) 90


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Attachment:
lines (2).jpg
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I am not able to get this chetan2u.. plz help
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GMAT Focus 1: 735 Q90 V89 DI81
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In the figure, what is the value of a ? 09 Oct 2018, 03:18
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saurabh9gupta
Bunuel

In the figure, what is the value of a ?

(A) 30
(B) 45
(C) 60
(D) 72
(E) 90


Show Spoiler
Attachment:
lines (2).jpg
I am not able to get this chetan2u.. plz help
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Three lines are crossing each other, so you have opposite angles that should be same...l and m gives you b=3c, m and n gives you a=2b..
So a=2b=2*3c=6c..
Take left side of line l all three angles should add up to 180, so a+b+6c=180....6c+3c+6c=180......15c=180....c=12
a=6c=6*12=72

D
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In the figure, what is the value of a ? 09 Oct 2018, 08:23
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Bunuel

In the figure, what is the value of a ?

(A) 30
(B) 45
(C) 60
(D) 72
(E) 90


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Attachment:
lines (2).jpg
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Vertically Opposite angles are equal
a = 2b
b = 3c

i.e. a = 2b = 6c

Also, a+6c + 3c = 180

i.e. a+9c = 180

i.e. 6c+9c = 180

i.e. 15c = 180

i.e. c = 12

i.e. a = 6c = 12*6 = 72

Answer: Option D

saurabh9gupta I hope this explanation helps... :)
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In the figure, what is the value of a ? 12 Oct 2018, 07:50
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Bunuel

In the figure, what is the value of a ?

(A) 30
(B) 45
(C) 60
(D) 72
(E) 90


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Attachment:
lines (2).jpg
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Since vertical angles are equal in measure, we have 3c = b, a = 2b and the unmarked angle (between b and 2b) measures 6c degrees.

Therefore, we can say:

b + 2b + 6c = 180

3b + 6c = 180

b + 2c = 60

Substituting 3c for b, we have:

3c + 2c = 60

5c = 60

c = 12; thus, b = 36

Since a = 2b, a = 72.

Answer: D
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In the figure, what is the value of a ? 13 Oct 2018, 02:01
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\(a+6c+3c=180\)

\(a+9c=180\)


from given information:

\(a=2b\)

\(b=\frac{a}{2}\)


\(3c=b\)

\(c=\frac{b}{3}\)

\(c=\frac{a}{6}\)


So

\(a+9(\frac{a}{6})=180\)

\(a+\frac{3a}{2}=180\)

\(2a+3a=360\)

\(5a=360\)

\(a=72\)
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In the figure, what is the value of a ? 06 Apr 2025, 06:58
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