Polygon Interior and Exterior Angle Sums
Polygon Interior and Exterior Angle Sums
\[\begin{aligned}
S_i &= (n-2)180^\circ \\
S_e &= 360^\circ
\end{aligned}\]
Variables
Si = sum of interior angles (deg)
Se = sum of exterior angles (deg)
n = number of sides
Description
What is this formula?
This set of formulas calculates the sum of the interior and exterior angles of a polygon using the number of sides.
When to use it
Use these formulas in geometry, mathematics education, engineering, and drafting when analyzing polygonal shapes.
Example
For a polygon with 8 sides:
Interior angle sum:
Si = (8-2)*180 = 1080°
Exterior angle sum:
Se = 360°
Applications
- Polygon analysis
- Geometric construction
- CAD and technical drawing
- Educational mathematics
- Architectural design
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