BdMO Online Forum

What is directed angle

It means the angle has an orientation based value, i.e. $\angle ABC=-\angle CBA$ Also see former $9-10$ Higher Math Geo book. In the beginning of trigonometry, there is a section about signed angles.

Also for simplicity, sometimes mod $\pi$ redian is also used. In that case $\pi - \angle ABC\equiv -\angle ABC\equiv \angle CBA\pmod \pi$

This is not a olympiad level question. So moving it to secondary.

To add just a little to what Adib said-
Anti-clockwise = positive, Clockwise = negative is the general convention while using the +/- sign.
I was going to post a link here but didn't find anything well-explained enough in google (at least in the first few links).

I think this might help...
Courtesy of R. A. Johnson, MAA, and, JSTOR :
http://www.jstor.org/stable/2973001