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In the figure, lines AB and DE are parallel. What is the measure of AB

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 57279
In the figure, lines AB and DE are parallel. What is the measure of AB  [#permalink]

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New post 18 Jul 2019, 22:26
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (01:25) correct 38% (02:44) wrong based on 24 sessions

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Duke & Cornell Moderator
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S
Joined: 29 May 2018
Posts: 88
Location: India
GMAT 1: 700 Q48 V38
GMAT 2: 720 Q49 V39
GPA: 4
Re: In the figure, lines AB and DE are parallel. What is the measure of AB  [#permalink]

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New post 19 Jul 2019, 13:46
Combining the information it can be seen that

for triangle CDE, we know all the angles as x=z=67.5 hence y=45

Sides CD and CE are equal=10

There will exist a unique triangle whose 2 sides and all angles are known. Hence, using law of cosine

de2= cd2+ de2 - 2 cd*de cos 45
de2= 200- 200/1.414
de2= 58.6
de= 7.65

Using AAA similarity, ABC is similar to CDE

The ratio of sides is proportional for similar triangles:

CD/DE= CB/AB

Without info on CB or AC, AC can not be deduced

Answer E
GMAT Club Bot
Re: In the figure, lines AB and DE are parallel. What is the measure of AB   [#permalink] 19 Jul 2019, 13:46
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In the figure, lines AB and DE are parallel. What is the measure of AB

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