Answer
See below
Work Step by Step
(a)
A polygon is a two-dimensional figure, which is of two types - 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.
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\[{{360}^{o}}\].
Hence,the polygons surround each vertex is hexagon with 6 sides and with three sides, which are called triangle.
(b)
The number of angles that come together at each vertex is four in which two angles are formed by the hexagon, two angles are formed by the triangle.
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 that is 6.
\[\begin{align}
& m\measuredangle =\frac{720{}^\circ }{6} \\
& =120{}^\circ
\end{align}\]
A measure of an angle of a regular triangle will be determined by dividing the sum of the measures of all angles, which is \[{{180}^{o}}\] by its sides i.e., 3.
\[\begin{align}
& m\measuredangle =\frac{180{}^\circ }{3} \\
& =60{}^\circ
\end{align}\]
Hence, the measure of the angle at each vertex of a polygon is\[{{120}^{o}}\], \[{{60}^{o}}\]
(c)
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.
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\[360{}^\circ \].
To check whether a tessellation can be created or not, add the measurement of the angles as mentioned below:
\[\begin{align}
& \text{Sum}=60{}^\circ +60{}^\circ +120{}^\circ +120{}^\circ \\
& ={{360}^{o}}
\end{align}\]
Hence, tessellation can be created as the measurement of all the angles is\[360{}^\circ \].