Q:

# Draw the following regular polygons inscribed in a circle:pentagonhexagondecagondodecagon (12-gon)For each polygon, include the following information in the paragraph box below:What was the central angle you used to locate the vertices? Show your calculation.What is the measure of each interior angle of the polygon? Show your calculation.What is the relationship between the central angle and the interior angle?As the number of sides increases, how do the angles change? please help !! PLZ HELP WILL MARK BRAINLIEST

Accepted Solution

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Answer:first attachment has pentagon and decagonsecond attachment has hexagon and dodecagoncomputation info explained belowStep-by-step explanation:1, 2. Central Angle, Interior AngleSee the 3rd attachment for the values. (Angles in degrees.)The central angle is 360°/n, where n is the number of vertices. For example, the central angle in a pentagon is 360°/5 = 72°.The interior angle is the supplement of the central angle. For a pentagon, that is 180° -72° = 108°.These formulas were implemented in the spreadsheet shown in the third attachment.3. Angles vs. Number of SidesThe size of the central angle is inversely proportional to the number of sides. In degrees, the constant of proportionality is 360°._____Comment on the drawingsThe drawings are made by a computer algebra program that is capable of computing the vertex locations around a unit circle based on the number of vertices. The only "work" required was to specify the number of vertices the polygon was to have. The rest was automatic. The above calculations describe how the angles are computed. Converting those to Cartesian coordinates for the graphics plotter involves additional computation and trigonometry that are beyond the required scope of this answer.These figures can be "constructed" using a compass and straightedge. No knowledge of angle measures is required for following the recipes to do that.