Explanation:
We can use then the formula to find the interior angle of a regular polygon to check if a figure will tessellate. Interior angle of a regular polygon = [180 × (n-2)] / n A couple of examples showing how to use the formula above to determine which figures will tessellate.
Example #1
Determine whether a regular pentagon will tessellate
A pentagon has 5 sides, so n = 5.
Interior angle of the pentagon = [180 × (5-2)] / 5
Interior angle of the pentagon = [180 × 3] / 5
Interior angle of the pentagon = 540 / 5
Interior angle of the pentagon = 108 degrees
There is no way to make 360 with 108 since 108 + 108 + 108 = 324 and 108 + 108 + 108 + 108 = 432
Therefore the pentagon will not tessellate as you can see below:
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