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In the figure, AD and BC are lines intersecting at O. What i

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Carcass
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In the figure, AD and BC are lines intersecting at O. What i [#permalink] New post   22 Sep 2018, 09:21
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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
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A
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jpalaciosm
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Re: In the figure, AD and BC are lines intersecting at O. What i [#permalink] New post   01 Jul 2020, 22:50
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To solve this problem, we should work with opposite angles which values are the same.

This means that:
5y/2=5x+5a
Reducing
y/2=x+a

a=y/2-x............................(1)

Also

y=2x+30
Reducing this expression, we obtain

y/2=x+15 .........................(2)

Replacing (2) in (1)

a=(x+15)-x

a=15

Answer=A
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Re: In the figure, AD and BC are lines intersecting at O. What i [#permalink] New post   13 Feb 2021, 01:34
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Carcass wrote:
Attachment:
#GREpracticequestion In the figure, AD and BC are lines intersecting at O.jpg


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


Vertically opposite angles are equal

So, \(y = 2x + 30\)
and, \(5x + 5a\) = \(\frac{5(2x +30)}{2}\)
\(10x + 10a\) =\(10x + 150\)
\(10a = 150\)
\(a = 15\)

Hence, option A
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Re: In the figure, AD and BC are lines intersecting at O. What i [#permalink] New post   08 Jun 2022, 17:48
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the figure, AD and BC are lines intersecting at O. What i [#permalink]
08 Jun 2022, 17:48
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