Triangles

[kanha81]

Please see the attached diagram.

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

a) 45
b) 60
c) 67.5
d) 112.5
e) 135

[ManSab]

CE = DE
we know y = 45 ,
sum of angles of triangle is 180
180-45 = 135

Isoscles triangle rule: angles opposite to equal sides are equal.
135/2 = 67.5 , other two angles of triangle ECD = 67.5 each, let us say v and z.

Now, AB and CE are parallel lines. We know each parallel lines intersect the third line at the same angle.
this means v=x=67.5


please correct if I am wrong.
Thanks

[jk2010]

Someone please help me with my logic here....

Since AB and CE are parallel, shouldn't angles ECB and ABC be equal? If so, x=90.

I have Y=45, EDC = 45, ECD = 90

AEC = 135, EAB = 45, ECB = 90, X=90

Where am I going wrong? Thanks.

[rros0770]

Agree with ManSab.

JK-

"I have Y=45, EDC = 45, ECD = 90"

This would be the case if CD=CE


Question states that CE=DE
Therefore EDC and ECD are the angles that are equal to each other, so:
Y= 45, EDC = 67.5, ECD = 67.5

Hope that helped.

[jk2010]

Yes thanks..... I am slapping myself in the head right now. I had it fixed in my head that ECD was a 45-45-90.

[Scott@TargetTestPrep]

Please see the attached diagram.

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

a) 45
b) 60
c) 67.5
d) 112.5
e) 135

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 (180 - 45) / 2 = 135/2 = 67.5 degrees.

Answer: C