Interior Angles of Polygons Starting with a Triangle

Logic, Mathematics
Regular polygons are closed curves with a set number of sides and interior angles, each of identical value. How can one calculate the interior angles of polygons? An equilateral triangle has three equal sides and three equal interior angles. Each angle is 60° or π/3 radians, adding up to 180° or π radians total. A square has four equal sides and four equal interior angles. Each interior angle is 90° or π/2 radians, adding up to 360° or 2π radians total. Interior Angles of Polygons A short chart of additional polygons with their interior angles provides the following data: Pentagon 5 interior angles of 108° (540° or 3π radians total) Hexagon 6 interior angles of 120° (720° or 4π radians total) Heptagon 7 interior angles of about 128.57° (900° or 5π radians total)…
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What are Radians? Where Do They Come From?

Consider a simple equilateral triangle (a triangle that has 3 equal sides and 3 equal angles). Most high-school students know the three angles of such a triangle are 60 degrees (60°) each, for a total of 180°. But degrees is not the only unit used to quantify an angle. Alternately radians can be used. What are radians? Are they just another number? Where do they come from? Degrees Before we get into radians, however, let’s consider where degrees came from, and why it may not be the best choice for the measurement of an angle. If you are facing north and turn to the east, you have turned 90 degrees. Now turn south and you’ve turned another 90 degrees. Turn west, another 90 degrees. Continue the turn so you once…
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