Constructing the figure from the question
From the question, the triangle in the tessellation is an equilateral triangle
Hence, since equilateral triangle has all it angles to be equal then
[tex]x=60^{\circ}[/tex]
From the tesselation,
[tex]x+y+z=360^{\circ}[/tex]
But z = y
Therefore
[tex]\begin{gathered} x+2y=360 \\ 60+2y=360 \\ 2y=360-60 \\ 2y=300 \\ y=\frac{300}{2} \\ y=150 \end{gathered}[/tex]
Hence one of the angle of the other shape of the tesselation is 150 degrees
Now we need to find the number of sides of the shape
applying number of sides of a polygon
Let n = number of sides
Then
[tex]sum\text{ of interior angles =180(n-2)}[/tex]
But
sum of interior angles = n x 150 degrees
Therefore, we have
[tex]150n=180(n-2)[/tex]
Now, we solve for n
[tex]\begin{gathered} 150n=180n-360 \\ 360=180n-150n \\ 360=30n \\ n=\frac{360}{30} \\ n=12 \end{gathered}[/tex]
Hence the number of sides of the polygon is 12
A polygon having 12 sides is called dodecagon
Hence the answer is regular dodecagon
