Each Interior Angle (Regular)

This formula finds the size of one angle inside a regular polygon, meaning a shape with all sides and all angles equal. It works because any polygon with n sides can be divided into n-2 triangles from one corner, and those triangles together have a total of (n-2) × 180°; dividing by n gives the same interior angle at each vertex. The result must be less than 180° because the shape is convex and each angle fits around the inside without flattening out.

Use this when you know the number of sides of a regular polygon and need the measure of one interior angle. It is common in geometry problems, tessellation questions, design work, and checks involving polygons in exams or construction drawings.

• Using the formula for irregular polygons, where angles are not all equal
• Forgetting to subtract 2 from the number of sides before multiplying by 180°
• Mixing up interior angles with exterior angles, which add to 360° in a regular polygon