What is the size of the interior angle of a regular 12-sided polygon?

The interior angle of a regular shape is the angle found on the inside of the shape at each of its corners. A twelve-sided regular polygon is too complex to remember its geometric rules so we must divide it into smaller shapes of which we know something about the geometry. If we draw a line from each of the corners of this shape to the centre point we have created 12 identical isosceles triangles. There are two main geometric rules for isosceles triangles that we know which will help us calculate the interior angles. One; the sum of all angles will add up to 180 degrees (this is true for any triangle), and two; two of the angles are equal in size.

We can calculate the size of the smaller angle of the triangles as all 12 of these angles form a whole circle (360 degrees). Thus 360 divided by 12 is the size of the angle: 30 degrees. The other two angles must add up to 150 degrees, as 180 minus 30 equals 150. As the angles are identical we can calculate them by dividing 150 by 2: 75 degrees. As the interior angle of the shape is made of two of these angles we can calculate it by doubling the size of the angle. 75 times 2 equals 150 degrees. This is the size of the interior angle.