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

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)

Name	Sides	Shape	Interior Angle
		If it is a Regular Polygon..
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	10¹⁰⁰		~180°
n-gon	n		(n-2) × 180° / n