paper test geometry question

[ifthyder]

explain plz?

[codesnooker]

It is very simple problem based on parallelism and isosceles triangle property concept.

Given things:

i) AB || CE
ii) angle (y) = 45 degree.
iii) CE = ED

Also, angle (y) + angle (ECD) + angle (CDE) = 180 degree.

Now as CE = ED, therefore angle (ECD) = angle (CDE), by the property of isosceles triangle.

Therefore, angle (ECD) = (180 - 45)/2 = 67.5 degree.

Now as AB || CE, therefore by parallel lines properties, angle (x) = 67.5

[ifthyder]

thanks