Q: Why do the interior angle in an equilateral triangle and the interior angle of a regular hexagon tessellate?

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If it's interior angle is a factor of 360 then it will tessellate such as a square, a regular hexagon and an equilateral triangle.

Equilateral triangle, square and regular hexagon.

Equilateral triangle, square and regular hexagon.

Only an equilateral triangle, square and a regular hexagon can be used to make regular tessellations but there are innumerable polygonal and non-polygonal shapes which will tessellate by themselves, and others which will tessellate along with other shapes.

idont know people i really search ervery single information but theres nothing its a hexagon,square,circleor an equilateral triangle

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If it's interior angle is a factor of 360 then it will tessellate such as a square, a regular hexagon and an equilateral triangle.

An equilateral triangle, a square and a hexagon.

Equilateral triangle, square and regular hexagon.

Equilateral triangle, square and regular hexagon.

No only three can tesselate. they are: An equilateral triangle, a square and a 6 sided hexagon.

Equilateral triangle, square and regular hexagon.

It will tessellate if its vertices divide into 360 degrees evenly. The only regular polygons that will tessellate are an equilateral triangle, a square and a regular hexagon. There are other, non-regular, polygons that will tessellate.

Yes, a hexagon can be equilateral if it has six equal sides, which will give it six equal interior angles

Any where the angles of 3 or more of the shape that meet at a point can add up to 360°, namely an equilateral triangle, a square and a hexagon.

I think it has something to do with their angles all adding up to 360 degrees! If you take the internal angle measure of a hexagon (150 I think) and add it up to the 90 degrees in a square and the 60 degrees in an equilateral triangle, you get 360! so it all works out. But squares and hexagons can only tessellate with equilateral triangles so bear that in mind. I think it has something to do with their angles all adding up to 360 degrees! If you take the internal angle measure of a hexagon (150 I think) and add it up to the 90 degrees in a square and the 60 degrees in an equilateral triangle, you get 360! so it all works out. But squares and hexagons can only tessellate with equilateral triangles so bear that in mind.

No. It doesn't tessellate. (You cannot tile out an area with small decagons.) The sum of the measures of the interior angles of a polygon with n sides is (n-2)180° So the sum of all the interior angles in a decagon add up to (8x180)= 1440°. To find only ONE angle you need to divide 1440 by 10, yielding 144. 360 divided by 144 is 2.5, not an integral number. This shows that a decagon doesn't tessellate. In fact, only the regular (equilateral) triangle, the square, and the regular hexagon will tessellate. For example: The sum of all the interior angles in a triangle add up to 180. 180 divided by 3 is 60. 360 divided by 60 is 6 (an integral number). This shows that a triangle will tessellate. Try this method with a square (or hexagon) and you will see that it works (square 360/90=4 and hexagon 360/120=3).

Only an equilateral triangle, square and a regular hexagon can be used to make regular tessellations but there are innumerable polygonal and non-polygonal shapes which will tessellate by themselves, and others which will tessellate along with other shapes.