The figures in a tessellation do not overlap or leave gaps. If the figures are polygons, the sum of the measures of the angles around any vertex in the tessellation must be 360.
Tessellation
Not a tessellation
Does a regular 18-gon tessellate? Explain.
How can you use the fact that the sum of the measures of the angles around a vertex in a tessellation is 360?
First, determine the measure of each angle of a regular 18-gon. Then check whether a multiple of this measure is 360.
Think | Write |
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All angles of a regular 18-gon have the same measure. | Let
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Use the Polygon Angle-Sum Theorem to find a. Substitute 18 for n and simplify. |
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Is there a multiple of 160 that equals 360? |
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Two copies of the 18-gon will leave gaps. Three copies of the 18-gon will overlap. | There is no multiple of 160 that equals 360, so a regular 18-gon does not tessellate. |