Concept

The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides.

Explanation

1️⃣ Definition of Exterior Angles

• An exterior angle is formed by extending one side of a polygon at a vertex.
• The exterior and interior angles at a vertex are supplementary (sum to 180°).

2️⃣ Full Rotation Around the Polygon

• Imagine walking around the polygon and turning at each vertex to follow the exterior angles.
• By the time you complete one full circuit, the total turn is 360°.

3️⃣ Mathematical Proof

• A convex polygon with n sides has interior angles summing to:
  180(n−2)degrees
• Since each exterior angle is:
  Exterior Angle=180°−Interior Angle
• Summing all exterior angles across all vertices results in:
  360°

Key Takeaways

✅ The sum of exterior angles of any polygon (regular or irregular) is always 360°.
✅ This rule applies to all polygons, including triangles, quadrilaterals, pentagons, etc.
✅ Each exterior angle of a regular polygon is 360°/n, where n is the number of sides.