
A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself!
Simple Polygon (this one's a Pentagon)  Complex Polygon (also a Pentagon) 
A convex polygon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.
If there are any internal angles greater than 180° then it is concave. (Think: concave has a "cave" in it)
Vertical Angles are the angles opposite each other when two lines cross
They are called "Vertical" because they share the same Vertex (or corner point)
In this example, a° and b° are vertical angles. The interesting thing here is that vertical angles are equal: a° = b°(in fact they are congruent angles) 
If it is a Regular Polygon..  
Name  Sides  Shape  Interior Angle 

Triangle (or Trigon)  3  60°  
Quadrilateral (or Tetragon)  4  90°  
Pentagon  5  108°  
Hexagon  6  120°  
Heptagon (or Septagon)  7  128.571°  
Octagon  8  135°  
Nonagon (or Enneagon)  9  140°  
Decagon  10  144°  
Hendecagon (or Undecagon)  11  147.273°  
Dodecagon  12  150°  
Triskaidecagon  13  152.308°  
Tetrakaidecagon  14  154.286°  
Pentadecagon  15  156°  
Hexakaidecagon  16  157.5°  
Heptadecagon  17  158.824°  
Octakaidecagon  18  160°  
Enneadecagon  19  161.053°  
Icosagon  20  162°  
Triacontagon  30  168°  
Tetracontagon  40  171°  
Pentacontagon  50  172.8°  
Hexacontagon  60  174°  
Heptacontagon  70  174.857°  
Octacontagon  80  175.5°  
Enneacontagon  90  176°  
Hectagon  100  176.4°  
Chiliagon  1,000  179.64°  
Myriagon  10,000  179.964°  
Megagon  1,000,000  ~180°  
Googolgon  10^{100}  ~180°  
ngon  n  (n2) × 180° / n 