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

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Bunuel
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In the figure above, if AB||CE, CE = DE, and y = 45, then x = [#permalink] New post   16 Sep 2018, 02:18
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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


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BrentGMATPrepNow
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In the figure above, if AB||CE, CE = DE, and y = 45, then x = [#permalink] New post   Updated on: 17 May 2021, 07:19
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Bunuel wrote:

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
Show Spoiler
Attachment:
GAMT_PS_1248.png


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


Also given: CE = DE
When we add this information to our diagram, we see that ∆ECD is an isosceles triangle, which means ∠CDE = x°

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

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Originally posted by BrentGMATPrepNow on 11 Apr 2020, 08:12.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:19, edited 1 time in total.
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dave13
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In the figure above, if AB||CE, CE = DE, and y = 45, then x = [#permalink] New post   16 Sep 2018, 03:15
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Bunuel wrote:

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


Show Spoiler
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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Re: In the figure above, if AB||CE, CE = DE, and y = 45, then x = [#permalink] New post   16 Sep 2018, 04:37
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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
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Nipunh1991
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Re: In the figure above, if AB||CE, CE = DE, and y = 45, then x = [#permalink] New post   30 Apr 2020, 17:11
Bunuel wrote:

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


Show Spoiler
Attachment:
GAMT_PS_1248.png


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
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Re: In the figure above, if AB||CE, CE = DE, and y = 45, then x = [#permalink] New post   03 Dec 2020, 12:46
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?
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Re: In the figure above, if AB||CE, CE = DE, and y = 45, then x = [#permalink] New post   13 Dec 2020, 06:20
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Bunuel wrote:

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


Show Spoiler
Attachment:
GAMT_PS_1248.png

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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Re: In the figure above, if AB||CE, CE = DE, and y = 45, then x = [#permalink] New post   26 Jan 2023, 11:33
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Re: In the figure above, if AB||CE, CE = DE, and y = 45, then x = [#permalink]
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