Understanding Interior and Exterior Angles of Polygons: Learn the formulas for calculating angles in polygonsSarah ThompsonJan 14, 2026Table of ContentsQuick SummaryFormula for Interior AnglesFormula for Exterior AnglesExamples and ApplicationsFAQFree Smart Home PlannerAI-Powered smart home design software 2025Home Design for FreeQuick Summary- The sum of interior angles of an n-sided polygon is (n − 2) × 180°, and each interior angle of a regular polygon is [(n − 2) × 180°] / n.- The sum of exterior angles of any polygon is 360°, and each exterior angle of a regular polygon is 360° / n.- Example values: a pentagon’s interior angles sum to 540°, and a hexagon’s each exterior angle is 60°.When it comes to polygons, understanding the formulas for interior and exterior angles is crucial for both design and analysis. The interior angle of a polygon is the angle formed inside the polygon at each vertex, while the exterior angle is the angle formed outside the polygon when one side is extended. Knowing these angles can help in various applications such as architecture and interior design.Formula for Interior AnglesThe formula for calculating the sum of the interior angles of a polygon is given by the equation: Sum of Interior Angles = (n - 2) × 180°, where n is the number of sides in the polygon. For instance, a pentagon (5 sides) would have a sum of interior angles equal to (5 - 2) × 180° = 540°. To find each interior angle of a regular polygon, simply divide the sum by the number of sides: Interior Angle = (Sum of Interior Angles) / n.Formula for Exterior AnglesThe sum of the exterior angles of any polygon is always 360°, regardless of the number of sides. This means for a regular polygon, each exterior angle can be calculated by dividing the total sum by the number of sides: Exterior Angle = 360° / n. For example, a hexagon (6 sides) would have each exterior angle measuring 360° / 6 = 60°.Examples and ApplicationsUnderstanding these formulas is essential, especially when designing spaces. For instance, when planning a room layout in an irregular-shaped space, knowing the angles can help ensure that furniture fits perfectly. In future projects, consider how these angles impact your designs.FAQwelcome to CoohomHome Design for FreePlease check with customer service before testing new feature.