which of the following is the number of sides a polygon can have to form a regular tessellations
A polygon can form a regular tessellation only if the sum of its interior angles is a divisor of 360 degrees. Therefore, the number of sides a polygon can have to form a regular tessellation are the factors of 360 degrees.
The factors of 360 are:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
So, the number of sides a polygon can have to form a regular tessellation are any of the above numbers.
To form a regular tessellation, the number of sides a polygon can have must meet a certain requirement. Here are the possibilities:
1. Triangle (Equilateral): A regular tessellation can be formed with equilateral triangles, as three triangles can meet at each vertex. Each interior angle of an equilateral triangle measures 60 degrees.
2. Square: A regular tessellation can be formed with squares, as four squares can meet at each vertex. Each interior angle of a square measures 90 degrees.
3. Hexagon: A regular tessellation can be formed with regular hexagons, as three hexagons can meet at each vertex. Each interior angle of a regular hexagon measures 120 degrees.
So, the possible number of sides a polygon can have to form a regular tessellation are 3 (triangle), 4 (square), and 6 (hexagon).