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
Triangles
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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
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
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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.
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.
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.
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.
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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
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