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What is the angle sum around a vertex in a tessellation?
In a tessellation, the angle sum around a vertex depends on the type of polygons used in the tessellation. For regular polygons, the angle sum around a vertex is always 360 degrees. This is because each interior angle of a regular polygon is the same, so when multiple regular polygons meet at a vertex in a tessellation, the angles add up to 360 degrees.
Because the figures in a tessellation do not overlap or leave gaps the sum of the measures of the angles around any vertex must be?
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.
What are facts about tessellation?
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 360º which is what all of the angles should come out to.
Why will a equilateral triangle tessellate?
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.
What is the sum of the measures of its exterior angles one at each vertex of a regular n-gon?
360
