Complete the table below. Show all solutions.
| | Sides | Interior Angle sum | Measure of ONE INTERIOR Angle (Regular Polygon) | Exterior Angle Sum | Measure of ONE EXTERIOR Angle (Regular Polygon) |
|---|-------|----------------------|-------------------------------------------------|--------------------|-------------------------------------------------|
| 1) | | | | 340 | |
| 2) | 14 | | | | |
| 3) | 24 | | | | |
| 4) | 17 | | | | |
| 5) | 8 | 1080° | | | |
| 6) | 7 | 900° | | | |
| 7) | 3 | 5040° | | | |
| 8) | 11 | 1620° | | | |
| 9) | 12 | | 150° | | |
| 10)| | | 120° | | |
| 11)| 15 | | 156° | | |
| 12)| | | | | 10° |
| 13)| 360/x | | | | 7.2° |
| 14)| | | | | 90° |
| 15)| | | | | |
Answer (2)
Analyze the table and use formulas to calculate missing values related to polygons' properties.
Explanation
Problem Analysis Let's analyze the given table and fill in the missing values step by step. We will use the formulas for the interior angle sum, measure of one interior angle, exterior angle sum, and measure of one exterior angle of a polygon.
Examples
Understanding polygons and their angles is useful in architecture, where designers need to calculate angles for constructing buildings with specific shapes. For example, knowing the angles of a regular hexagon is crucial when designing hexagonal tiles or structures. This knowledge ensures that the structures are stable and aesthetically pleasing.
We calculated missing values in the polygon table using the properties of polygons, including formulas for interior and exterior angles based on the number of sides. Each polygon's interior angle sums and measures were derived, completing the table with accurate results. These calculations highlight key geometric principles that are applicable in various real-world contexts.
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