Because the measure of each angle in a pentagon is 108 degrees, which 360 can't be divided evenly by, so pentagons don't tessellate because their is always a little extra space left over.
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:L I Need Help With This Do Hexagons, Tesselate ?
Triangles, squares and hexagons will tesselate 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.
no
regular pentagons
equilateral triangles and regular pentagons