A square tile, a regular hexagon tile, an equilateral triangle tile, and a regular n-sided polygon tile share a common vertex. There are no gaps or overlaps between the tiles. What is n?

Guest Jul 13, 2021

#1**+2 **

Angle of the vertex of the combined shapes so far (without n sided) = $360 - (90 + 120 + 60) = 90.$ so we need a shape that has angle side 90 to finish the 360 degrees. therefore, it is a square: with 4 sides. it is an n-sided polygon, so **n = 4**

HighSchoolDx Jul 13, 2021

#1**+2 **

Best Answer

Angle of the vertex of the combined shapes so far (without n sided) = $360 - (90 + 120 + 60) = 90.$ so we need a shape that has angle side 90 to finish the 360 degrees. therefore, it is a square: with 4 sides. it is an n-sided polygon, so **n = 4**

HighSchoolDx Jul 13, 2021