# Answer to Question #29497 in Geometry for carmen ella

Question #29497

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

Expert's answer

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.

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.

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