0
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.
Still curious? Ask our experts.
Chat with our AI personalities
Blake
Steve
Ezra
Add your answer:
Earn +20 pts
What is the sum of the angles at any vertex in a tessellation?
It is 360 degrees.
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 does the Polygon Exterior Angle Sum Theorem say?
Theorem 6-1-2; Polygon Exterior Angle Sum Theorem:The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360 degrees.
What is the sum of the angle measures at each vertex of a tessellation?
It's all based on what you tesselate. If 360 degrees makes a full circle or rotation, then you know that for every vertex intersecting it is 360 divided by the quantity of vertexes. For example, if we had a tesselation of only triangles, we would have 6 vertexes. We know this because it takes 6 equilateral triangles to make a hexagon. So, we simply do 360, which are the degrees we have to go around, divided by 6, the total vertices (the plural of vertex), we would get 60. We know this is true because the sum of the degrees in all vertices in a triangle HAS to be 180.
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.
