Answer
Sum of tessellation is\[363{}^\circ \]and it is fake because the sum is not equivalent to\[360{}^\circ \].
Work Step by Step
A polygon is a two-dimensional figure, which is of two types that is a regular polygon and an irregular polygon. A regular polygon is a figure in which all the sides are of the same length. In irregular polygon, all sides are of different length.
A polygon with three sides is called a triangle. A polygon with four sides is called rectangle or quadrilateral. A polygon with five sides is called pentagon and so on. A tessellation is a type of art that is used to define a relationship between geometry and the visual arts. Tessellations are created by repeated use of same figures that will leave no gap and no overlaps and thus cover the whole plane.
The number of angles measured at a vertex Ais three which is formed by octagon, hexagon,and pentagon. A measure of an angle of a regular hexagon will be determined by dividing the sum of the measures of all angles, which is\[720{}^\circ \]by its sides, i.e., 6.
\[\begin{align}
& m\measuredangle A=\frac{720{}^\circ }{6} \\
& =120{}^\circ
\end{align}\]
A measure of an angle of a regular octagon will be determined by dividing the sum of the measures of all angles, which is \[1,080{}^\circ \] by its sides, i.e., 8.
\[\begin{align}
& m\measuredangle A=\frac{1080{}^\circ }{8} \\
& =135{}^\circ
\end{align}\]
A measure of an angle of a regular pentagon will be determined by dividing the sum of the measures of all angles, which is \[540{}^\circ \] by its sides, i.e., 5.
\[\begin{align}
& m\measuredangle A=\frac{540{}^\circ }{5} \\
& =108{}^\circ
\end{align}\]
The sum of the measures of the angles at a vertex A:
\[\begin{align}
& \text{Sum of }m\measuredangle A=108{}^\circ +120{}^\circ +135{}^\circ \\
& =363{}^\circ
\end{align}\]
To create a tessellation, the primary requirement is that the sum of the measures of the angles of a regular polygon that are together at each vertex must be\[360{}^\circ \]. The sum of the measure of angles at a vertex A is\[363{}^\circ \], which can cause overlaps of \[3{}^\circ \] which shows that a tessellation is fake.
