Given a table of polygons
For the first row,
Given that the 1 exterior angle of the polygon is given, to find the number of sides, n, the formula is
[tex]\begin{gathered} \text{One exterior angle}=\frac{360\degree}{n} \\ 120\degree=\frac{360\degree}{n} \\ \text{Crossmultiply} \\ 120\degree\times n=360\degree \\ \text{Divide both sides by 120} \\ n=\frac{360\degree}{120\degree} \\ n=3 \end{gathered}[/tex]
The number of sides, n, of the polygon is three, thus it is a triangle.
A regular triangle has
[tex]\begin{gathered} 3\text{ sides} \\ Sum\text{ of interior angles is 180}\degree \\ One\text{ interior angle is 60}\degree \\ Sum\text{ of exterior angles is 360}\degree \\ \text{One exterior angle is 120}\degree \end{gathered}[/tex]
For the second row
Given that sum of the interior angles of the polygon is 720°, to find the number of sides of the polygon,
Using the formula to find the sum of the interior angles of a polygon which is
[tex]\begin{gathered} Sum\text{ of interior angles}=(n-2)180\degree \\ 720\degree=(n-2)180\degree \\ \text{Divide both sides by 180}\degree \\ \frac{720\degree}{180\degree}=\frac{(n-2)180\degree}{180\degree} \\ 4=n-2 \\ \text{Collect like terms} \\ n=4+2 \\ n=6\text{ sides} \end{gathered}[/tex]
Since the number of sides is 6, thus, it is a hexagon.
For a regular hexagon, is tas
[tex]\begin{gathered} 6\text{ sides} \\ \text{Sum of interior angles is 720}\degree \\ One\text{ interior angle is }120\degree \\ \text{Sum of exterior angles is 360}\degree \\ \text{One exterior angle is 60}\degree \end{gathered}[/tex]
The table is shown below
