Math Problem Statement
Solution
The table you've provided appears to be a math problem related to polygons, specifically asking to complete information about different polygons based on their number of sides. Let's fill in the missing information.
Columns of the table:
- Number of Sides: Given in the table.
- Kind of Polygon: Name based on the number of sides.
- Number of Triangles: This is given by .
- Sum of Interior Angles: This is given by .
- Measure of Each Angle in a Regular Polygon: This is given by .
Let's fill in the table:
Number of Sides | Kind of Polygon | Number of Triangles | Sum of Interior Angles (in degrees) | Measure of Each Angle in a Regular Polygon (in degrees) |
---|---|---|---|---|
3 | Triangle | 1 | ||
4 | Quadrilateral | 2 | ||
5 | Pentagon | 3 | ||
6 | Hexagon | 4 | ||
8 | Octagon | 6 | ||
10 | Decagon | 8 | ||
12 | Dodecagon | 10 |
Would you like a detailed explanation on how each of these calculations is performed, or do you have any specific questions about this table?
Here are 5 related questions you might consider:
- How do you calculate the sum of interior angles for any polygon?
- Why does the number of triangles matter in calculating the sum of interior angles?
- How does the measure of each angle change as the number of sides increases in a regular polygon?
- What is the relationship between the number of sides and the name of the polygon?
- Can you derive the formula for the measure of each angle in a regular polygon?
Tip:
Remember, the exterior angle of a regular polygon is always . This can be useful for solving various problems involving polygons.
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Math Problem Analysis
Mathematical Concepts
Geometry
Polygons
Interior Angles
Regular Polygons
Formulas
Number of Triangles = (Number of Sides - 2)
Sum of Interior Angles = (Number of Sides - 2) × 180°
Measure of Each Angle in a Regular Polygon = Sum of Interior Angles / Number of Sides
Theorems
Polygon Interior Angle Sum Theorem
Suitable Grade Level
Grades 6-8
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