What can I do to know if a polygon will tessellate?

Answer 1

If the polygon is irregular it isn't always easy to tell. But if it is regular, divide 360° by the number of degrees in one angle. If it divides exactly it will tesselate.

Equilateral triangle = 360/60 = 6. It will tessellate.
Square = 360/90 = 4. It will tessellate.
Hexagon = 360/120 = 3. It will tessellate.

That's it for regular polygons.

The quotient tells you how many polygons come together at one vertex.