Answer :
To complete the table, we know the number of sides and the number of interior angles for each polygon. We shall proceed by inserting these values into the table.
Additionally, we will name the sides and the interior angles for each polygon:
1. For the Triangle:
- Number of sides: 3
- Number of interior angles: 3
- Name the sides: [tex]\( a, b, c \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma \)[/tex]
2. For the Quadrilateral:
- Number of sides: 4
- Number of interior angles: 4
- Name the sides: [tex]\( a, b, c, d \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta \)[/tex]
3. For the Pentagon:
- Number of sides: 5
- Number of interior angles: 5
- Name the sides: [tex]\( a, b, c, d, e \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon \)[/tex]
4. For the Hexagon:
- Number of sides: 6
- Number of interior angles: 6
- Name the sides: [tex]\( a, b, c, d, e, f \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta \)[/tex]
5. For the Heptagon:
- Number of sides: 7
- Number of interior angles: 7
- Name the sides: [tex]\( a, b, c, d, e, f, g \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta \)[/tex]
6. For the Octagon:
- Number of sides: 8
- Number of interior angles: 8
- Name the sides: [tex]\( a, b, c, d, e, f, g, h \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta \)[/tex]
7. For the Nonagon:
- Number of sides: 9
- Number of interior angles: 9
- Name the sides: [tex]\( a, b, c, d, e, f, g, h, i \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota \)[/tex]
8. For the Decagon:
- Number of sides: 10
- Number of interior angles: 10
- Name the sides: [tex]\( a, b, c, d, e, f, g, h, i, j \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota, \kappa \)[/tex]
Let's fill out the table now:
\begin{center}
\begin{tabular}{|l|c|c|c|c|}
\hline
\multicolumn{1}{|c|}{\begin{tabular}{c}
Name of \\
Polygon
\end{tabular}} & \begin{tabular}{c}
Number \\
of sides
\end{tabular} & \begin{tabular}{c}
Number of \\
interior angles
\end{tabular} & \begin{tabular}{c}
Name the \\
sides
\end{tabular} & \begin{tabular}{c}
Name the interior \\
angles
\end{tabular} \\
\hline Triangle & 3 & 3 & [tex]\(a, b, c\)[/tex] & [tex]\(\alpha, \beta, \gamma\)[/tex] \\
\hline Quadrilateral & 4 & 4 & [tex]\(a, b, c, d\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta\)[/tex] \\
\hline Pentagon & 5 & 5 & [tex]\(a, b, c, d, e\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon\)[/tex] \\
\hline Hexagon & 6 & 6 & [tex]\(a, b, c, d, e, f\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta\)[/tex] \\
\hline Heptagon & 7 & 7 & [tex]\(a, b, c, d, e, f, g\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta\)[/tex] \\
\hline Octagon & 8 & 8 & [tex]\(a, b, c, d, e, f, g, h\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta\)[/tex] \\
\hline Nonagon & 9 & 9 & [tex]\(a, b, c, d, e, f, g, h, i\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota\)[/tex] \\
\hline Decagon & 10 & 10 & [tex]\(a, b, c, d, e, f, g, h, i, j\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota, \kappa\)[/tex] \\
\hline
\end{tabular}
\end{center}
This table shows the number of sides, the number of interior angles, and the naming conventions for both sides and angles of various polygons.
Additionally, we will name the sides and the interior angles for each polygon:
1. For the Triangle:
- Number of sides: 3
- Number of interior angles: 3
- Name the sides: [tex]\( a, b, c \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma \)[/tex]
2. For the Quadrilateral:
- Number of sides: 4
- Number of interior angles: 4
- Name the sides: [tex]\( a, b, c, d \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta \)[/tex]
3. For the Pentagon:
- Number of sides: 5
- Number of interior angles: 5
- Name the sides: [tex]\( a, b, c, d, e \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon \)[/tex]
4. For the Hexagon:
- Number of sides: 6
- Number of interior angles: 6
- Name the sides: [tex]\( a, b, c, d, e, f \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta \)[/tex]
5. For the Heptagon:
- Number of sides: 7
- Number of interior angles: 7
- Name the sides: [tex]\( a, b, c, d, e, f, g \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta \)[/tex]
6. For the Octagon:
- Number of sides: 8
- Number of interior angles: 8
- Name the sides: [tex]\( a, b, c, d, e, f, g, h \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta \)[/tex]
7. For the Nonagon:
- Number of sides: 9
- Number of interior angles: 9
- Name the sides: [tex]\( a, b, c, d, e, f, g, h, i \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota \)[/tex]
8. For the Decagon:
- Number of sides: 10
- Number of interior angles: 10
- Name the sides: [tex]\( a, b, c, d, e, f, g, h, i, j \)[/tex]
- Name the interior angles: [tex]\( \alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota, \kappa \)[/tex]
Let's fill out the table now:
\begin{center}
\begin{tabular}{|l|c|c|c|c|}
\hline
\multicolumn{1}{|c|}{\begin{tabular}{c}
Name of \\
Polygon
\end{tabular}} & \begin{tabular}{c}
Number \\
of sides
\end{tabular} & \begin{tabular}{c}
Number of \\
interior angles
\end{tabular} & \begin{tabular}{c}
Name the \\
sides
\end{tabular} & \begin{tabular}{c}
Name the interior \\
angles
\end{tabular} \\
\hline Triangle & 3 & 3 & [tex]\(a, b, c\)[/tex] & [tex]\(\alpha, \beta, \gamma\)[/tex] \\
\hline Quadrilateral & 4 & 4 & [tex]\(a, b, c, d\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta\)[/tex] \\
\hline Pentagon & 5 & 5 & [tex]\(a, b, c, d, e\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon\)[/tex] \\
\hline Hexagon & 6 & 6 & [tex]\(a, b, c, d, e, f\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta\)[/tex] \\
\hline Heptagon & 7 & 7 & [tex]\(a, b, c, d, e, f, g\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta\)[/tex] \\
\hline Octagon & 8 & 8 & [tex]\(a, b, c, d, e, f, g, h\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta\)[/tex] \\
\hline Nonagon & 9 & 9 & [tex]\(a, b, c, d, e, f, g, h, i\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota\)[/tex] \\
\hline Decagon & 10 & 10 & [tex]\(a, b, c, d, e, f, g, h, i, j\)[/tex] & [tex]\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \iota, \kappa\)[/tex] \\
\hline
\end{tabular}
\end{center}
This table shows the number of sides, the number of interior angles, and the naming conventions for both sides and angles of various polygons.
