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

Question

https://gmatclub.com/forum/download/file.php?id=43693 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 GAMT_PS_1248.png

BrentGMATPrepNow · Accepted Answer

Given: y = 45 and AB||CE 
When a transversal intersects two parallel lines (as shown below), we get several equal angles. 
So we also know that ∠ECD =   x°   .
We get the following
 https://i.imgur.com/tZpr4JW.png

Also given: CE = DE 
When we add this information to our diagram, we see that ∆ECD is an isosceles triangle, which means ∠CDE =   x°   
 https://i.imgur.com/ezMDTaf.png 
Since angles in a triangle add to 180°, we can write: 45 + x + x = 180
Simplify: 45 + 2x = 180
Subtract 45 from both sides: 2x = 135
Divide both sides by 2 to get: x = 67.5

Answer: C

Cheers, 
Brent

RELATED VIDEO
 https://www.youtube.com/watch?v=F26uam3kmCU

dave13 · Answer

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

HITMAN09 · Answer

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

Nipunh1991 · Answer

Since Y = 45 and the Line CE and DE are equal. Triangle CED is an isosceles triangle, which would mean Angle ECD and Angle EDC are equal.
Since Y is 45 and the sum of all angles of the triangle is 180.
Angle EDC + Angle ECD = 180 - 45 = 135
Angle EDC = Angle ECD = 67.5 (135/2)

Now Since Line AB and EC are parallel Angle ECD = Angle CBA = 67.5

Answer is C

Hope it helps a little

ra96 · Answer

I understand the concept of the isosceles triangles but in this case how are we supposed to be sure that the two angles that are equal within the triangle are angle ECD and angle EDC and not that there are two y's in the triangle?

ScottTargetTestPrep · Answer

Solution:

Since AB || CE, we see that triangles ABD and ECD are similar. Therefore, angle A = angle CED and angle B = angle ECD. Furthermore, since CE = DE, triangle ECD is an isosceles triangle, and angle ECD = angle CDE. Since we are given that angle CED = y = 45 degrees, then angles ECD and CDE are each (180 - 45) / 2 = 135/2 = 67.5 degrees. Since angle B = angle ECD, angle B = x = 67.5 degrees.

Answer: C

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

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