Why do interior and exterior angles add to 180°?

At each vertex of a polygon, the interior angle and its adjacent exterior angle together form a straight line (180°), so they're always supplementary.

Does this work for irregular polygons?

No, this formula assumes a regular polygon where all sides and angles are equal. Irregular polygons can have interior angles that sum to the same total but aren't evenly distributed.

Regular Polygon Interior Angle Calculator

Calculate the measure of each interior angle and exterior angle of a regular polygon (a polygon with all equal sides and angles), given the number of sides. Useful for geometry, design, and construction layouts.

Inputs

Results

Interior Angle: 120 °
Exterior Angle: 60 °
Sum of All Interior Angles: 720 °

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Formula

Interior angle = (n − 2) × 180° / n, Exterior angle = 360° / n

Learn How This Works

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