How many sides has an equiangular polygon if one of its exterior angles is 25 5/7?

Step One

Figure out the interior angle

25 5/7 = 25.714285 repeating. The interior angle is the supplement of this angle.

180 - 25.714285 = 154.2857

The formula relating the number of sides and the interior equal angle is

interior equal angle = 180 (1 - 2/n) where n is the number of sides. (Google equiangular polygon to find this formula.)

154.2857 / 180 = 1 - 2/n)

0.8571428 = 6/7 = 1 - 2/n

1/7 = 2/n

n = 14 sides

This figure is regular as well as equiangular.