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Gary is using a combination of regular polygonal tiles for his kitchen floor. He begins the tessellation at a vertex by placing two triangles.

Which two polygons should he use to fill up the vacant space at the vertex and make it possible to tessellate the floor?

2 hexagons because 360 – (60 + 60) = 2 x 120

2 squares because 180 = 90 + 90

1 square and a hexagon because 360 – (60 + 60 + 60) = 60 + 120

1 triangle and a hexagon because 180 = 60 + 120

Question

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Gary is using a combination of regular polygonal tiles for his kitchen floor. He begins the tessellation at a vertex by placing two triangles. 
  
Which two polygons should he use to fill up the vacant space at the vertex and make it possible to tessellate the floor? 

 2 hexagons because 360 – (60 + 60) = 2 x 120 

 2 squares because 180 = 90 + 90 

 1 square and a hexagon because 360 – (60 + 60 + 60) = 60 + 120 

 1 triangle and a hexagon because 180 = 60 + 120