Complete the table below. Show all solutions.
| | # Sides | Interior Angle Sum | Measure of ONE INTERIOR Angle (Regular Polygon) | |
|---|---|---|---|---|
| 1) | n | [tex](n-2) 180^{\circ}[/tex] | [tex]\frac{(n-2) 180^{\circ}}{n-}[/tex] | [tex]\frac{360}{n}[/tex] |
| 2) | 14 | | | |
| 3) | 24 | | | |
| 4) | 17 | | | |
| 5) | 8 | [tex]1080^{\circ}[/tex] | | |
| 6) | 7 | [tex]900^{\circ}[/tex] | | |
| 7) | 30 | [tex]5040^{\circ}[/tex] | | |
| 8) | | [tex]1620^{\circ}[/tex] | | |
| 9) | 12 | | [tex]150^{\circ}[/tex] | |
| 10) | | | [tex]120^{\circ}[/tex] | |
| 12) | | [tex]\frac{360}{x}[/tex] | [tex]156^{\circ}[/tex] | |
Answer (2)
We completed the table using formulas for polygons, calculating the Interior Angle Sum, Measure of ONE INTERIOR Angle, and Measure of ONE EXTERIOR Angle for each specified number of sides. The calculations show the various properties of polygons from 7 to 30 sides and fill in other gaps based on known angles. Students can use these automatic relationships to understand how polygons behave depending on their side counts.
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Fills in the missing values in the table using the formulas for interior angle sum, measure of one interior angle, and measure of one exterior angle of a polygon.
Explanation
Introduction and Strategy We will complete the table by calculating the missing values for each row using the provided formulas. The formulas relate the number of sides of a polygon to its interior angle sum, the measure of one interior angle (for a regular polygon), and the measure of one exterior angle.
Examples
Understanding polygon properties is useful in architecture for designing buildings with specific angles and shapes, in art for creating tessellations and geometric patterns, and in engineering for structural analysis and design.
