5.1 Polygon Sum Conjecture


Is there a Polygon Sum Fornula

Number of sides of Polygon 3      4      5      6      7        8   ....    n Sum of measures of angles 180  360  540  720  900  1,080 If a polygon has n sides, it is called an n-gon. A general formula for the sum of the angle measures of a polygon in terms of the number of sides, n is (n-2)180 The amount of triangles I have created is 4 triangles. The amount of triangles the diagonals have created in the dodecagon in the right is 10 triangles. The number of triangles do relate to n because if you put this in the general formula mentioned earlier, it will tell you how many degrees is in the n-gon. Quadrilateral Sum Conjecture The sum of the measure of the four interior angles of any quadrilateral is 360 degrees Pentagon Sum Conjecture The sum of the measures of the five interior angles of any pentagon is 540 degrees Polygon Sum Conjecture The sum of the measure of the n interior angles of an n-gon is (n-2)180