In the diagram below, AB and EF are parallel. If angle ABC = 120 degrees, angle BCD = 180 degrees, and angle ECD = 55 degrees, then what is angle CEF, in degrees?
Continue line EF to the left so that it intersects line BCD at point X
Since FEX is parallel to AB, angle(CXE) = 180o - angle(ABC) = 180o - 120o = 60o.
In triangle(CXE), angle(CXE) = 60o and angle(ECD) = 55o, so angle(XEC) = 65o.
This means that angle(CEF) = 115o.