\[\begin{aligned}
\theta_i &= \frac{(n-2)180^\circ}{n} \\
\theta_e &= \frac{360^\circ}{n}
\end{aligned}\]
Variables
θiinterior angle (deg)
θeexterior angle (deg)
nnumber of sides
Description
What is this formula?
This set of formulas calculates the interior and exterior angles of a regular polygon using the number of sides.
When to use it
Use these formulas in geometry, engineering, architecture, and drafting when analyzing polygons with equal sides and equal angles.
Example
For a regular hexagon with 6 sides:
Interior angle:
θi = ((6-2)*180)/6 = 120°
Exterior angle:
θe = 360/6 = 60°
Applications
- Geometric analysis
- CAD and technical drawing
- Architecture and design
- Polygon construction
- Educational mathematics