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# In the figure, AD and BC are lines intersecting at O. What is the valu

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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09 Oct 2018, 00:03
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:08) correct 27% (02:35) wrong based on 49 sessions

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In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15

(B) 30

(C) 45

(D) 60

(E) 135

Attachment:

lines (1).jpg [ 20.85 KiB | Viewed 550 times ]

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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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09 Oct 2018, 02:22
Bunuel wrote:

In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15
(B) 30
(C) 45
(D) 60
(E) 135

Attachment:
lines (4).jpg

Vertically Opposite angles are equal
5x + 5a = 5y/2

i.e. 2x + 2a = y

Also, 5x + 5a + 2x + 30 = 180

i.e. 7x + 5a = 150

Also, y = 2x + 30

i.e. 2x + 2a = 2x + 30

i.e. a = 15

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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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09 Oct 2018, 03:37
Bunuel wrote:

In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15
(B) 30
(C) 45
(D) 60
(E) 135

Attachment:
lines (4).jpg

5x+5a=5y/2
2x+30=y

Substitute value of y

10x+10a= 10x+150
10a=150
A=15

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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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09 Oct 2018, 16:43
Bunuel wrote:

In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15

(B) 30

(C) 45

(D) 60

(E) 135

a) $$y+\frac{5y}{2}=180$$ or, y=360/7 (Angles on one side of a straight line always add to 180 degrees)
b) y=2x+30 or, $$x=\frac{75}{7}$$ (opposite angles are congruent)
c) 5x+5a+2x+30=180 or, 7x+5a=150 or, 5a=150-75=75 or, a=15

Ans. (A)
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Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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15 Oct 2018, 23:51
1
Bunuel wrote:

In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15
(B) 30
(C) 45
(D) 60
(E) 135

Attachment:
lines (4).jpg

Dear Moderator,
Same question seems to have been duplicated in the link below , you may wish to merge the same, Thank you.

https://gmatclub.com/forum/in-the-figur ... l#p2148445
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- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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15 Oct 2018, 23:53
stne wrote:
Bunuel wrote:

In the figure, AD and BC are lines intersecting at O. What is the value of a ?

(A) 15
(B) 30
(C) 45
(D) 60
(E) 135

Attachment:
lines (4).jpg

Dear Moderator,
Same question seems to have been duplicated in the link below , you may wish to merge the same, Thank you.

https://gmatclub.com/forum/in-the-figur ... l#p2148445

________________
Merged. Thank you.
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Intern
Joined: 08 Oct 2018
Posts: 3
Re: In the figure, AD and BC are lines intersecting at O. What is the valu  [#permalink]

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16 Oct 2018, 09:39
we can say, 5x+5a=5y/2
=>5(x+a)=5y/2
=>2x+2a=y

again, y=2x+30
=>2x+2a=2x+30
=>a=15
Ans A

Posted from my mobile device
Re: In the figure, AD and BC are lines intersecting at O. What is the valu   [#permalink] 16 Oct 2018, 09:39
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