📐 Polygon Angle Sum 📚 Grade 4-5 ⏱ 6 min
Sum of Interior Angles of Any Polygon
After the triangle (180°) and quadrilateral (360°), the pattern continues — there is a general formula for any number of sides.
The growth pattern
A triangle (3 sides) — 180°. A quadrilateral (4 sides) — 360°. Each extra side adds another 180°.
💡 Formula: angle sum = (number of sides − 2) × 180°. Check for a triangle: (3−2)×180=180. For a quadrilateral: (4−2)×180=360.
Practice
A pentagon: (5−2)×180=540°. A hexagon: (6−2)×180=720°.
FAQ
Does this formula work for any polygon?
Yes, for convex polygons with any number of sides, the formula always applies.