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In the figure above, if AB||CE, CE = DE, and y = 45, then x =

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 55670
In the figure above, if AB||CE, CE = DE, and y = 45, then x =  [#permalink]

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New post 16 Sep 2018, 02:18
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:53) correct 21% (01:59) wrong based on 131 sessions

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Joined: 09 Mar 2016
Posts: 1279
In the figure above, if AB||CE, CE = DE, and y = 45, then x =  [#permalink]

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New post 16 Sep 2018, 03:15
1
Bunuel wrote:
Image
In the figure above, if AB||CE, CE = DE, and y = 45, then x =

A. 45
B. 60
C. 67.5
D. 112.5
E. 135


Attachment:
GAMT_PS_1248.png


if CE = DE it means that triangle CED is iscoseles triangle. this means that two angles will be equal.

also if AB||CE that means that two triangles are similar which means both triangles have the same angles

sum of degrees of any triangle is 180 degrees

hence

45+2x= 180
2x= 135
x = 67.5

hopefully i am not incorrect :lol:
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Joined: 20 Jun 2017
Posts: 14
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Re: In the figure above, if AB||CE, CE = DE, and y = 45, then x =  [#permalink]

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New post 16 Sep 2018, 04:37
3
Given
AB||CE,
CE = DE, and
y = 45

As the CE = DE , Angle ECD = Angle EDC ( Consider Angle ECD = M )

Sum of all angle of triangle - ECD is 180, therefore Angle (ECD + EDC + CED ) = 180
2M + 45 = 180 = M = 67.5

Further, as AB||CE, Angle ECD = Angle ABC
Hence X= 67.5%
Answer
GMAT Club Bot
Re: In the figure above, if AB||CE, CE = DE, and y = 45, then x =   [#permalink] 16 Sep 2018, 04:37
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In the figure above, if AB||CE, CE = DE, and y = 45, then x =

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