In the diagram(please see attachment), the exterior angles of triangle ABC are <FAC, <ACD, <ECB, <CBI, <HBA and <BAG. What about the angles <, <DCE, <HBI, are they not exterior?
Look at this webpage.
Note that $\displaystyle \angle GAB$ has a side of $\displaystyle \Delta ABC$, $\displaystyle \overline{AB}$, as a subset.
But $\displaystyle \angle GAH $ has no side of $\displaystyle \Delta ABC$, as a subset.
The definition of "exterior angle". is "
Exterior Angles of Polygons
"The Exterior Angle is the angle between any side of a shape,
and a line extended from the next side."
http://en.wikipedia.org/wiki/Internal_and_external
"an exterior angle (or external angle) is an angle formed by one side of a simple, closed polygon and a line extended from an adjacent side."
What you have is two "lines extended from adjacent sides".
This strictly a post script to both of the replies posted.
I have no idea what level we are actually dealing with.
I would like to nail a definition for an exterior angle of a convex polygon.
This is due to R.L.Moore by way of his student Ed Moise in ELEMENTRY GEOMETY: from an advanced standpoint.
We need to know what it means that two angles form a linear pair.
We say that $\displaystyle \angle XAB$ is an exterior angle if and only if that angle forms a linear pair with an interior of the polygon with vertex $\displaystyle A$