Only 22 Polygons Have Integer Angles

Rather than using the polygon calculator constantly, this table was created to show the angles for some of the more commonly encountered polygons.

There are just 22 polygons that have angles which are integers.

Note: the triangle is sometimes (though rarely) referred to as a trigon and
the square is sometimes referred to as a tetragon.

 Polygon       NAME Polygon     SIDES Each   Interior    ANGLE Central     ANGLE   Equals   Exterior     Angle = Interior       ANGLE     Total Triangle 3 60 120 180 Square 4 90 90 360 Pentagon 5 108 72 540 Hexagon 6 120 60 720 Octagon 8 135 45 1,080 Nonagon 9 140 40 1,260 Decagon 10 144 36 1,440 Dodecagon 12 150 30 1,800 Pentadecagon 15 156 24 2,340 Octadecagon 18 160 20 2,880 Icosagon 20 162 18 3,240 Icositetragon 24 165 15 3,960 Triacontagon 30 168 12 5,040 Triacontahexagon 36 170 10 6,120 Tetracontagon 40 171 9 6,840 Tetracontapentagon 45 172 8 7,740 Hexacontagon 60 174 6 10,440 Heptacontadigon 72 175 5 12,600 Enneacontagon 90 176 4 15,840 ***** 120 177 3 21,240 ***** 180 178 2 32,040 ***** 360 179 1 64,440