Angles ECD and CEF add to 180
40+140 = 180
So that means we have EF parallel to CD (due to the same side interior angle theorem)
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Angles BCE and ECD combine to 30+40 = 70, which is congruent to angle ABC = 70 as well.
In other words, this shows angle ABC = angle BCD. Both of these angles are alternate interior angles. Since they're congruent, they lead to AB being parallel to CD.
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So far we have
AB || CD
CD || EF
Using the transitive property, we can then link the two statements to say AB || EF. Think of a chain where CD is the common link. We go from AB to CD, then from CD to EF. So we can just take a single path from AB to EF.
It's like saying "P --> Q and Q --> R, therefore P --> R"
