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Sagot :
Alright, let’s complete the table step-by-step by identifying the names of the polygon, their corresponding number of sides, and their number of interior angles. Here, the number of sides is equivalent to the number of interior angles for each polygon.
Here is the filled-out table:
[tex]\[ \begin{array}{|l|c|c|c|c|} \hline \multicolumn{1}{|c|}{\text{Name of Polygon}} & \text{Number of sides} & \text{Number of interior angles} & \text{Name the sides} & \text{Name the interior angles} \\ \hline \text{Triangle} & 3 & 3 & \text{Sides} & \text{Angles} \\ \hline \text{Quadrilateral} & 4 & 4 & \text{Sides} & \text{Angles} \\ \hline \text{Pentagon} & 5 & 5 & \text{Sides} & \text{Angles} \\ \hline \text{Hexagon} & 6 & 6 & \text{Sides} & \text{Angles} \\ \hline \text{Heptagon} & 7 & 7 & \text{Sides} & \text{Angles} \\ \hline \text{Octagon} & 8 & 8 & \text{Sides} & \text{Angles} \\ \hline \text{Nonagon} & 9 & 9 & \text{Sides} & \text{Angles} \\ \hline \text{Decagon} & 10 & 10 & \text{Sides} & \text{Angles} \\ \hline \end{array} \][/tex]
For clarification, "Name the sides" indicates labeling the individual sides, which we can refer to generally as "Sides" since they're named based on their adjacency and relationships in the actual figures. Likewise, "Name the interior angles" can simply be referred to as "Angles" following their respective positions in each polygon.
Here's a more detailed breakdown:
1. Triangle:
- Number of sides: 3
- Number of interior angles: 3
- Sides: Typically named as Side 1, Side 2, Side 3
- Interior angles: Typically named as Angle 1, Angle 2, Angle 3
2. Quadrilateral:
- Number of sides: 4
- Number of interior angles: 4
- Sides: Side 1, Side 2, Side 3, Side 4
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4
3. Pentagon:
- Number of sides: 5
- Number of interior angles: 5
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5
4. Hexagon:
- Number of sides: 6
- Number of interior angles: 6
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6
5. Heptagon:
- Number of sides: 7
- Number of interior angles: 7
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6, Side 7
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6, Angle 7
6. Octagon:
- Number of sides: 8
- Number of interior angles: 8
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6, Side 7, Side 8
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6, Angle 7, Angle 8
7. Nonagon:
- Number of sides: 9
- Number of interior angles: 9
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6, Side 7, Side 8, Side 9
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6, Angle 7, Angle 8, Angle 9
8. Decagon:
- Number of sides: 10
- Number of interior angles: 10
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6, Side 7, Side 8, Side 9, Side 10
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6, Angle 7, Angle 8, Angle 9, Angle 10
This provides a comprehensive view of the polygons, fulfilling the requirement to complete the table with the given information.
Here is the filled-out table:
[tex]\[ \begin{array}{|l|c|c|c|c|} \hline \multicolumn{1}{|c|}{\text{Name of Polygon}} & \text{Number of sides} & \text{Number of interior angles} & \text{Name the sides} & \text{Name the interior angles} \\ \hline \text{Triangle} & 3 & 3 & \text{Sides} & \text{Angles} \\ \hline \text{Quadrilateral} & 4 & 4 & \text{Sides} & \text{Angles} \\ \hline \text{Pentagon} & 5 & 5 & \text{Sides} & \text{Angles} \\ \hline \text{Hexagon} & 6 & 6 & \text{Sides} & \text{Angles} \\ \hline \text{Heptagon} & 7 & 7 & \text{Sides} & \text{Angles} \\ \hline \text{Octagon} & 8 & 8 & \text{Sides} & \text{Angles} \\ \hline \text{Nonagon} & 9 & 9 & \text{Sides} & \text{Angles} \\ \hline \text{Decagon} & 10 & 10 & \text{Sides} & \text{Angles} \\ \hline \end{array} \][/tex]
For clarification, "Name the sides" indicates labeling the individual sides, which we can refer to generally as "Sides" since they're named based on their adjacency and relationships in the actual figures. Likewise, "Name the interior angles" can simply be referred to as "Angles" following their respective positions in each polygon.
Here's a more detailed breakdown:
1. Triangle:
- Number of sides: 3
- Number of interior angles: 3
- Sides: Typically named as Side 1, Side 2, Side 3
- Interior angles: Typically named as Angle 1, Angle 2, Angle 3
2. Quadrilateral:
- Number of sides: 4
- Number of interior angles: 4
- Sides: Side 1, Side 2, Side 3, Side 4
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4
3. Pentagon:
- Number of sides: 5
- Number of interior angles: 5
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5
4. Hexagon:
- Number of sides: 6
- Number of interior angles: 6
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6
5. Heptagon:
- Number of sides: 7
- Number of interior angles: 7
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6, Side 7
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6, Angle 7
6. Octagon:
- Number of sides: 8
- Number of interior angles: 8
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6, Side 7, Side 8
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6, Angle 7, Angle 8
7. Nonagon:
- Number of sides: 9
- Number of interior angles: 9
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6, Side 7, Side 8, Side 9
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6, Angle 7, Angle 8, Angle 9
8. Decagon:
- Number of sides: 10
- Number of interior angles: 10
- Sides: Side 1, Side 2, Side 3, Side 4, Side 5, Side 6, Side 7, Side 8, Side 9, Side 10
- Interior angles: Angle 1, Angle 2, Angle 3, Angle 4, Angle 5, Angle 6, Angle 7, Angle 8, Angle 9, Angle 10
This provides a comprehensive view of the polygons, fulfilling the requirement to complete the table with the given information.
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