Q: What is the sum of the angles at any vertex in a tessellation?

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360 degrees, but this assumes that there are any angles. There need not be any angles - as illustrated by MC Escher in his set of Symmetry artwork.

Hi im bob

Some facts on tessellations are that there are different types of tessellations such as regular and semi-regular. In tessellations, each vertex will have a sum of 360ΓΒΊ which is what all of the angles should come out to.

Each angle in an equilateral triangle is 60 degrees. In order to create a regular tessellation of an area, we need for the angles of the polygons we are putting near each other to sum to 360 degrees. If you place six equilateral triangles so that all of them share a vertex, and each triangle is adjacent to two others, you get 60*6 = 360 degrees in that vertex. Please see related link for a demo of a triangular tessellation.

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The angles at any point is space add to 360 degrees. So, at any vertex in a tessellation, the angles of the vertices meeting there must sum to 360 degrees.

Yes. Regular or irregular, the angles at vertices must sum to 360 deg otherwise you will have gaps in the tessellation.

360 degrees, but this assumes that there are any angles. There need not be any angles - as illustrated by MC Escher in his set of Symmetry artwork.

The sum of the angles around a vertex point in a plane will always be 360o. Picture a bicycle wheel with all its spokes radiating out from the hub. Now pick two spokes to form a vertex. Find the angle of your vertex, and then subtract it from 360o. As there are 360o in a circle, and your figure (the vertex) is a slice of the circle, its angle plus all the rest of the arc about the vertex will sum to 360o. If you've discovered the angle of your vertex, you cannot help but find the sum of the rest of the angles (if there are more than one) around your vertex.

The total angles around a point is 360 degrees. Since there can be no gaps or angles, all of the angles meeting at any vertex must sum to 360 degrees.

Hi im bob

Some facts on tessellations are that there are different types of tessellations such as regular and semi-regular. In tessellations, each vertex will have a sum of 360ΓΒΊ which is what all of the angles should come out to.

No, complementary angles do not need to have the same vertex. Complementary angles are comprised of any two angles whose sum is 90 degrees. The definition of a complementary angle does not say that it needs to have the same vertex.

The sum of the exterior angles of any polygon add up to 360 degrees

The exterior angles of any polygon add up to 360 degrees

With exterior angles measured as in the related link (extending an imaginary line out from the vertex, so that the interior and exterior at the vertex add to 180Â°), the sum of exterior angles of any polygon is 360Â°: Interior / Exterior ______/............. Now if you are saying the exterior angle is all the way around the vertex, then you need to add 180Â° for each vertex. So 360Â° + 57*(180Â°) = 10620Â°.

The sum of the exterior angles of a convex polygon which has sides and one angle at each vertex is 360 degrees.