Question

Determine all possible values for size of three regular polynomials n₁​≤n₂​≤n₃​ For the 3 regular polynomials attached at each vertex (so their angle sums add to 360 degrees at each vertex) which cover the entire plane.

Answer 1

The possible values for the sizes of three regular polygons attached at each vertex, whose angle sums add to 360 degrees at each vertex, are n₁ = 60 degrees, n₂ = 60 degrees, and n₃ = 60 degrees.

Step-by-step explanation:

To determine all possible values for the sizes of three regular polygons, we need to consider the sum of the interior angles at each vertex. Since the polygons are regular, the sum of the interior angles at each vertex is 360 degrees.

For a triangle, which is a three-sided regular polygon, the sum of the interior angles is 180 degrees. Therefore, for three regular polygons attached at each vertex, the possible values for the sizes of the polygons would be n₁ = 60 degrees, n₂ = 60 degrees, and n₃ = 60 degrees.

The sizes of the polygons can't be greater than 180 degrees each or less than 60 degrees each, because those values would not satisfy the condition of three angles adding up to 360 degrees at each vertex.