What is the total of the interior angles of a hexagon?

Answer 1

The are two trapezoids in a hexagon, which is 4 triangles, and 4x180= 720 degrees. For any N-sided polygon, it is (N-2)*180°. See related question for further explanation. By "hexigon" I assume this was a 'typo' for "hexagon". In that case the answer is 720.

The interior angles I of regular polygons with nsides is given by:

I = ((n-2)/n)*180°

Thus the total T of the interior angles is given by:

n*I

The following table give values of interior angle and total of all angles for various regular polygons. As can be seen, as the number of side get larger and larger, the interior angle approaches 180°. It will only reach 180° when n is infinite. Likewise the total of interior angles also approaches infinity.

{| |- | N-Polygon Interior Angle Total All Angles 3 60 180 4 90 360 5 108 540 6 120 720 7 128.571429 900 8 135 1080 9 140 1260 10 144 1440 11 147.272727 1620 12 150 1800 13 152.307692 1980 14 154.285714 2160 15 156 2340 16 157.5 2520 17 158.823529 2700 18 160 2880 19 161.052632 3060 20 162 3240 30 168 5040 35 169.714286 5940 40 171 6840 45 172 7740 50 172.8 8640 60 174 10440 70 174.857143 12240 80 175.5 14040 90 176 15840 100 176.4 17640 200 178.2 35640 300 178.8 53640 400 179.1 71640 500 179.28 89640 1000 179.64 179640 2000 179.82 359640 3000 179.88 539640 4000 179.91 719640 5000 179.928 899640 6000 179.94 1079640 7000 179.948571 1259640 8000 179.955 1439640 9000 179.96 1619640 10000 179.964 1799640 20000 179.982 3599640 30000 179.988 5399640 40000 179.991 7199640 50000 179.9928 8999640 60000 179.994 10799640 70000 179.994857 12599640 80000 179.9955 14399640 90000 179.996 16199640 100000 179.9964 17999640

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