Answer
See below
Work Step by Step
(a)
In the present case, the entire figure is made up of triangles and squares. Even the vertex is surrounded either by a square or a triangle. Thus, there are only two types of regular polygons that surround each vertex.
(b)
Since, there are two angles. Each angle is equal to angle in a square and is equal to that of a right angle. It implies that the angle will be either \[60{}^\circ \] or\[90{}^\circ \]. Accordingly, the angles at vertex of tessellation will be\[~60{}^\circ ,60{}^\circ ,60{}^\circ ,90{}^\circ \text{and 9}0{}^\circ \].
Hence, the number of angles that come together at each vertex is 5 and the measures of the angles are\[~60{}^\circ \],\[~60{}^\circ \],\[~60{}^\circ \] ,\[~60{}^\circ \]and \[~60{}^\circ \].
(c)
: Since, the sum of measures of all the angles at any vertex of tessellation is\[360{}^\circ \].In order to determine whether the tessellation is possible or not. Now, compute the measures of all the angles at any vertex using the equation as shown below:
\[60{}^\circ +60{}^\circ +60{}^\circ +90{}^\circ +90{}^\circ ={{360}^{\circ }}\]
Since the sum of measures of all the angles at any vertex is\[360{}^\circ \], the tessellation is supposed to be possible.
