EOB and AOC are supplementary angles

I believe you want to know the condition that makes EOB and AOC supplementary angles.

Angles are said to be supplementary when their measures add up to 180.

So, for angles EOB and AOC to be supplementary:

measure angle EOB + measure angle AOC = 180 degrees

Examples that might lead to this:

EOB = 140 degrees and AOB = 40 degrees

EOB = 90 degrees and AOB = 90 degrees

EOB = 100 degrees and AOB = 80 degrees