Question

Which of the following regular polygons will not tessellate by itself?


triangle
square
hexagon
decagon

Answer 1

decagon

Answer 2

Triangles, squares and hexagons will tessellate with themselves. If you want to know why, calculate the angle measure for each of these shapes and you will see that each is a factor of 360. The same cannot be said for pentagons, heptagons, etc.
So that is the answer.
But not completely, especially for triangles because they do not have to be "regular" with 3 equal angles.
In fact any triangle of any shape will tessellate with triangles congruent with the original. Congruent means that the triangles have to have exactly the same shape and size.