Why can any shape tessellate?

Answer 1

Not all shapes can tessellate. For example a pentagon will not tessellate.

Only those shapes where the angles of the vertices which meet sum to 360° (a full turn) will tessellate.

For example, with a regular hexagon, each angle is 120° and when three come together they form 3×120° = 360° and so will tessellate, but with an octagon, each angle is 135°; two such angles form 2×135° = 270°, but three such angles form 3×135° = 405° - two octagons will lay together with a gap, but three octagons will overlap: they cannot tessellate; however, 360° - 270° = 90° which is the angle of a square, so octagons together with squares will tessellate.

Answer 2

The question cannot be answered sensibly because it is based on a false premise. Al shapes cannot tessellate!