Polygon – Interior and Exterior & Central Angles

Interior angle of a regular polygon

A regular polygon has all the interior angles same in measure, and all interior angles of polygon formed by each pair of adjacent sides.

When a polygon has n sides n vertices and n interior angles.

Interior angle = 180⁰ – Central angle (when central angle is known)

Each angle of a regular polygon = {(n-2)x180/n degrees 

Sum of interior angles = (n – 2)180 degrees.

where, n is number of sides.

Central angle of a regular polygon

A angle whose vertex is center of the regular polygon and sides are radii to the end points of the same side of the polygon, is known as the central angle of the regular polygon.

A central angle of regular polygon is 

Central angle = 360/n degrees 

where, n is number of sides of the regular polygon.

  Exterior angle of a regular polygon

In a regular polygon, all the exterior angles are same.

Exterior angle = central angle = 360/n degree

where, n is number of sides of the regular polygon.
Each exterior angle is equal to, dividing 360 by number of sides.