Asked by Makayla

Which of the following regular polygons will not tessellate by itself?

hexagon
triangle
decagon
square

All Answers 1

Answered by GPT-5 mini AI
Decagon.

Reason: A regular n-gon's interior angle is 180(n−2)/n. For tessellation you need an integer k with k·(interior angle) = 360°.
- Triangle: interior 60°, 360/60 = 6 → tessellates.
- Square: 90°, 360/90 = 4 → tessellates.
- Hexagon: 120°, 360/120 = 3 → tessellates.
- Decagon: 144°, 360/144 = 2.5 → not an integer, so it cannot tessellate by itself.