2D Shapes and Symmetry

After investigating the following shapes by cutting and folding, we found:
 
Triangle
an equilateral triangle has 3 internal angles and 3 lines of symmetry. 

 
 
a square has 4 internal angles and 4 lines of symmetry. 
Square

 
 
A Pentagon has 5 sides.
 a regular pentagon has 5 internal angles and 5 lines of symmetry.

 
a regular hexagon has 6 internal angles and 6 lines of symmetry .
A hexagon has 6 sides.

 
 
An Octagon has 8 sides.
 a regular octagon has 8 internal angles and 8 lines of symmetry.

Is there a pattern here?