Sum of Exterior Angles of Polygon = 360deg
Study Note: Sum of Exterior Angles of a Polygon
Formula : Sum of exterior angles of a polygon = 360â
Exterior Angle: The angle formed outside a polygon at each vertex (āĻŦāĻšāĻŋāĻāĻā§āĻŖ (Exterior Angle): āĻŦāĻšā§āĻā§āĻā§° āĻŦāĻžāĻšāĻŋā§°āĻ¤ āĻāĻ āĻŋāĻ¤ āĻā§āĻŖ)
Important Facts (Very Useful for Exams)
- Sum of all exterior angles (one at each vertex) = 360° (āĻĒā§ā§°āĻ¤āĻŋāĻā§ āĻļā§ā§°ā§āĻˇāĻŦāĻŋāĻ¨ā§āĻĻā§āĻ¤ āĻāĻāĻžāĻā§ āĻŦāĻšāĻŋāĻāĻā§āĻŖā§° āĻ¯ā§āĻāĻĢāĻ˛ = 360°)
- True for all polygons (triangle, square, pentagon…) (āĻ¸āĻāĻ˛ā§ āĻŦāĻšā§āĻā§āĻā§° āĻŦāĻžāĻŦā§ āĻ¸āĻ¤ā§āĻ¯)
- Independent of number of sides (āĻŦāĻžāĻšā§ā§° āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻāĻĒā§°āĻ¤ āĻ¨āĻŋā§°ā§āĻā§° āĻ¨āĻā§°ā§)
- Interior angle + Exterior angle = 180° (linear pair) (āĻāĻŋāĻ¤ā§°ā§° āĻā§āĻŖ + āĻŦāĻžāĻšāĻŋā§°ā§° āĻā§āĻŖ = 180°)
Related Formula (Interior Angles) : Sum of interior angles = (n − 2) × 180° (āĻāĻŋāĻ¤ā§°ā§° āĻā§āĻŖā§° āĻ¯ā§āĻāĻĢāĻ˛ = (n − 2) × 180°)
Shortcut Formula (Regular Polygon) : Each exterior angle = 360° / n (āĻĒā§ā§°āĻ¤āĻŋāĻā§ āĻŦāĻšāĻŋāĻāĻā§āĻŖ = 360° ÷ n)
Examples : Practice
Ex 1. Find each exterior angle of a pentagon (n = 5) = 360° ÷ 5 = 72° (āĻĒāĻžāĻāĻāĻā§āĻā§° āĻĒā§ā§°āĻ¤āĻŋāĻā§ āĻŦāĻšāĻŋāĻāĻā§āĻŖ = 72°)
Ex 2. If each exterior angle = 60°, find number of sides n = 360 ÷ 60 = 6 sides (hexagon) (āĻĒā§ā§°āĻ¤āĻŋāĻā§ āĻŦāĻšāĻŋāĻāĻā§āĻŖ 60° āĻš’āĻ˛ā§ → āĻŦāĻžāĻšā§ = 6)
Trick : Full turn around = 360° (āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻāĻā§ā§° = 360°)