angles in polygons by chopping

what do you see here?

rhombuses?
rectangles?
equilateral triangles?
(bigger) right angled triangles?
trapezia?
kites?
arrowheads?
regular hexagons?

students could create their own shapes using four of the 30, 60, 90 triangles

an intention is that they then sum the angles at the corners to explore the angle sums of polygons (with various numbers of sides)
 

in the above resources the triangles' vertices do not all meet at the vertices of the polygons

so students will need to work out the angle sums of the polygons by deciding which of the 30, 60, 90 angles to use and which not to use

for the following resources, the vertices of the 30, 60, 90 triangles are all at the vertices of the polygons 

I think these are all the options for quadrilaterals and pentagons

I don't think this is all the options for hexagons (I gave up)