Question

does a regular 22-gon tessellate the plane? does a regular 40-gon tessellate the plane?

Answer 1

A tessellation is createdwhen a shape is repeated over and over again covering a plane without any gaps
or overlaps.
Since 180(x-2) equals how many degrees it has,
180(22-2)= 180(20)= 180 x 20= 3600
To find only ONE angle you need to divide 3600 by 22, yielding 163.6.
360 divided by 163.6 is 2.2 , not an integral number.
This shows that a 22-gon doesn't tessellate.
and
180(40-2)= 180(38)= 180 x 38= 6840
To find only ONE angle you need to divide 6840 by 40, yielding 171.
360 divided by 171 is 2.1 , not an integral number.
This shows that a 40-gon doesn't tessellate.