Find the correct angles to cut perfect geometric shapes including a pentagon, hexagon, heptagon, octagon, nonagon, decagon, and any other polygon.
![Wooden Hexagon Box](https://timbertopia.com/wp-content/uploads/2023/11/05487be3-5b22-474e-a346-91090c8f3206.jpeg)
Step One – Solve for X
The first step is to imagine there are a series of triangles that make up the polygon.
![Hexagon with triangles Hexagon with an triangles in the center](https://timbertopia.com/wp-content/uploads/2023/11/Perfect-Hexagons-1.jpg)
We know that the sum of the interior angles (in this case X) will always be 360. This means we can solve for X with this equation:
![number of sides solve for x](https://timbertopia.com/wp-content/uploads/2023/11/Screenshot-2023-11-13-7.40.28-PM.png)
In this case we have 6 sides so we know: X = 60
Step Two – Solve for Y
Next we need to solve for y which will be the angle of our miter cuts. To find this angle we’ll need to use the next equation:
![Calculate the interior angles of a polygon](https://timbertopia.com/wp-content/uploads/2023/11/Screenshot-2023-11-13-7.40.40-PM.png)
Since the interior angles of a triangle will always equal 180, we will need to subtract x from the first step and then divide by two because there are two equal y angles.
In our example hexagon, we would subtract 180 – 60 and then divide by two to get: y = 60
Surprise! They are equilateral triangles
All Kinds of Polygons
The calculation works the same for any polygon — as long as all the sides are the same length.
Now you can cut the sides to length and cut with your miter saw.