Interior Angles Sum

Sum of interior angles = (n − 2) × 180° where n is sides.

Formula: (n-2) × 180

Example: Pentagon (5 sides): (5-2)×180 = 540°

Exterior Angles Sum

Exterior angles always sum to 360° for ANY polygon.

Formula: Sum = 360°

Example: Regular Hexagon: Each exterior = 360/6 = 60°

Regular Polygons

All sides and angles are equal. Each interior angle = Sum ÷ n.

Formula: Int = (n-2)×180 / n

Finding Number of Sides

If you know the exterior angle, n = 360 ÷ exterior angle.

Formula: n = 360 / ext

Example: Exterior = 40° n = 360/40 = 9 sides

Interior + Exterior

At any vertex, the interior and exterior angles add to 180° (straight line).

Formula: Int + Ext = 180°

Example: Ext = 36° → Int = 144°

Tessellation

Regular polygons tessellate if their interior angle divides exactly into 360°.

Irregular Polygons

Sum rules still apply, but individual angles vary based on the specifics of the shape.