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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
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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18 Jul 2019, 22:26
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Difficulty:

35% (medium)

Question Stats:

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

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

(1) CD = 10
(2) z = 67.5

Attachment:

2019-07-19_0921.png [ 17.15 KiB | Viewed 260 times ]

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Re: In the figure, lines AB and DE are parallel. What is the measure of AB  [#permalink]

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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

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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