Respuesta :
the answer is 360 Since the regular polygons in a tessellation must fill the plane at each vertex, the interior angle must be an exact divisor of 360degrees.
In order for polygons to tessellate, the vertices of the polygons should come together at a single point forming 360 degrees.
What is vertices of the polygons?
Polygons are the closed shaped plane which has minimum three sides and angles. These sides are connected to each other to form a closed shape at the corner or vertex point.
Vertices of the polygons is the point, where the two adjacent sides are intersected each other. It can also be described as the point, where, two sides or edges meet each other are called the vertices of the polygon.
A regular tessellate is the symmetric, side to side tiling made by the number of regular polygons having the the same shape and size.
For example, lets take the regular polygon of with four sides equal to each other. Now in this squared shape polygon, the vertices meet at the points of 90 degree for the two adjacent sides.
Here, there is total 4 vertices points (corner). Therefore, the total angle is,
[tex]x=90+90+90+90=360^o[/tex]
Hence, in order for polygons to tessellate, the vertices of the polygons should come together at a single point forming 360 degrees.
Learn more about the vertices of the polygons here;
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