3. Polygon Sides Angle Sum Interior Angle
Triangle 3 180 60

8. Polygon Sides Angle Sum Interior Angle
Quadrilateral 4 360 90
Pentagon 5 540 108
Hexagon 6 720 120
Octagon 8 1080 135

12. Polygon Interior Angle
Pentagon 108
The interior angles do not add
108+108+108 = 324
up to 360o, therefore it means
108+108+108+108 = 432
that regular pentagons do not
tessellate.
Polygon Interior Angle
Octagon 135
The interior angles do not add
135+135 = 270 up to 360o, therefore it means
135+135+135 = 405 that regular octagons do not
tessellate.

14. Tessellation must tile a floor with no overlapping or gaps, and they
should be regular polygons.
To tessellate using the regular polygons, you need to use the ones that
their interior angles add up to 360 degrees.
For triangles: interior angle = 60 degrees
60+60+60+60+60+60 = 360
For squares: interior angle = 90 degrees
90+90+90+90 = 360
For hexagons: interior angle = 120 degrees
120+120+120 = 360
For pentagons: interior angle = 108 degrees
108+108+108 = 324

16. 6-3-6-3 TESSELLATION

17. Triangle’s interior angle: 60o
60o+120o+60o+120o
= 180o+180o
= 360o
Hexagon’s interior angle: 120o

18. Interior
angle of an
octagon:
135O
135o+90o+135o Interior
= 360o angle of a
square: 90O

19. Interior Interior
Interior
150o+120o+90o
angle of a angle of a
dodecagon: hexagon:
angle of a = 270o+90o
square: 90O
150O 120O = 360o