Which of the following polygons can tile the plane?
I: regular pentagon
II: regular hexagon
A) I only
B) II only
C) both I and II
D) neither

Question

Which of the following polygons can tile the plane? 
I: regular pentagon
II: regular hexagon
A) I only
B) II only
C) both I and II
D) neither

Quizplus · Accepted Answer

Only regular polygons with an interior angle that can divide into 360 degrees evenly can tile the plane without overlapping or leaving gaps. A regular pentagon has an interior angle of 108 degrees, which cannot fit evenly into 360 degrees. On the other hand, a regular hexagon has an interior angle of 120 degrees, which can fit evenly into 360 degrees. Therefore, a regular hexagon can tile the plane.

Which of the Following Polygons Can Tile the Plane