Perhaps someone can help me with this:
For simple closed curves on an orientable compact surface, if they form a bigon, then is it true that at the intersection points the orientations must be different?
To put this in context see http://www.math.uchicago.edu/~margalit/mcg/mcgv50.pdf ("Primer on Mapping Class Groups" by Farb and Margalit) page 73 end of the proof of prop.3.2. which states "in a true bigon, the orientations at the two intersection points are different,...".
Cheers!