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# In the figure above, line segments AD and BE intersect at C. What is

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Math Expert
Joined: 02 Sep 2009
Posts: 54371
In the figure above, line segments AD and BE intersect at C. What is  [#permalink]

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09 Aug 2017, 04:43
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Difficulty:

65% (hard)

Question Stats:

28% (01:32) correct 72% (01:25) wrong based on 56 sessions

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In the figure above, line segments AD and BE intersect at C. What is the value of x in terms of y?

(A) 85 – y
(B) 90 – y
(C) y + 15
(D) y + 25
(E) y + 25

Attachment:

2017-08-09_1259_001.png [ 12.92 KiB | Viewed 1351 times ]

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Re: In the figure above, line segments AD and BE intersect at C. What is  [#permalink]

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09 Aug 2017, 05:46
Lets consider angle c on both sides as p (since they opposite angles)

Now considering both the triangles separately, we get

x+85+p = 180 and y+110+p = 180

solving..
p = 70 - y. Putting this in first.

x+85+(70-y) = 180
x - y + 155 = 180
or
x = y +25

Both D and E are showing the same options.

So i believe we need to fix that
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In the figure above, line segments AD and BE intersect at C. What is  [#permalink]

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09 Aug 2017, 08:53
Bunuel wrote:

In the figure above, line segments AD and BE intersect at C. What is the value of x in terms of y?

(A) 85 – y
(B) 90 – y
(C) y + 15
(D) y + 25
(E) y + 25

Attachment:
2017-08-09_1259_001.png

$$\angle$$ ECD = 180 - (110+y) = 70 -y
$$\angle$$BCA =$$\angle$$ ECD = 70-y (Veritically opposite angles are equal )

$$\angle$$ BAC = x = 180 -( 85+70-y)
=> x = 180 - 155 +y
=> x = 25 + y

Answer D and E both are y+25 .

Bunuel, Can you please check as both options D and E are same here .
Also , vertex B in upper triangle is missing .
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Re: In the figure above, line segments AD and BE intersect at C. What is  [#permalink]

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11 Aug 2017, 21:06
Take Angle ACB as a .Angle DCE will also be a since they are vertically opposite .
From Tr.ACB x+a=95
FromTr.DCE y+a=70

Therefor X+a= y+a+25
And therefore x=y+25

Option D and E both are correct.

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Re: In the figure above, line segments AD and BE intersect at C. What is   [#permalink] 11 Aug 2017, 21:06
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