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# In the figure, what is the value of a ?

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In the figure, what is the value of a ?  [#permalink]

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09 Oct 2018, 00:45
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:40) correct 33% (02:06) wrong based on 33 sessions

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In the figure, what is the value of a ?

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

Attachment:

lines (2).jpg [ 21.36 KiB | Viewed 511 times ]

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Re: In the figure, what is the value of a ?  [#permalink]

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09 Oct 2018, 00:58
1
Bunuel wrote:

In the figure, what is the value of a ?

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

Attachment:
lines (2).jpg

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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Re: In the figure, what is the value of a ?  [#permalink]

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09 Oct 2018, 01:24
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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Re: In the figure, what is the value of a ?  [#permalink]

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09 Oct 2018, 02:11
Bunuel wrote:

In the figure, what is the value of a ?

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

Attachment:
lines (2).jpg

I am not able to get this chetan2u.. plz help
Math Expert
Joined: 02 Aug 2009
Posts: 7335
Re: In the figure, what is the value of a ?  [#permalink]

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09 Oct 2018, 02:18
saurabh9gupta wrote:
Bunuel wrote:

In the figure, what is the value of a ?

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

Attachment:
lines (2).jpg

I am not able to get this chetan2u.. plz help

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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Re: In the figure, what is the value of a ?  [#permalink]

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09 Oct 2018, 07:23
Bunuel wrote:

In the figure, what is the value of a ?

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

Attachment:
lines (2).jpg

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

saurabh9gupta I hope this explanation helps...
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Re: In the figure, what is the value of a ?  [#permalink]

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12 Oct 2018, 06:50
Bunuel wrote:

In the figure, what is the value of a ?

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

Attachment:
lines (2).jpg

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.

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Re: In the figure, what is the value of a ?  [#permalink]

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13 Oct 2018, 01:01
$$a+6c+3c=180$$

$$a+9c=180$$

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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Re: In the figure, what is the value of a ?   [#permalink] 13 Oct 2018, 01:01
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