I think this question is MUCH easier than it first appears to be.
The little tirangle and the big one are similar triangles BUT you do not need to use this fact.
1) Mark everything that you know on the diagram.
2) let distance MI=x and IN=y that will make it easier
3) Find missing angles using facts about angles on a transversal through parallel lines.
4) use these angles to deduce facts about side lengths.
5) You should now have algebraic expressions for lengths AM and AN and MN
6) add those lengths together and see what you get :))
Please no one answer over the top of me, I am trying to teach.
If you get stuck you can ask specific questions. :)