Polygon Angle Calculator

Regular Decagon (10 sides): Sum of interior angles = (10 - 2) x 180 = 1,440 degrees Each interior angle = 1,440 / 10 = 144 degrees Each exterior angle = 360 / 10 = 36 degrees Diagonals = 10(10-3)/2 = 35

A polygon is a closed two-dimensional shape made up of straight line segments. When all sides are equal in length and all interior angles are equal in measure, it is called a regular polygon. Understanding polygon angles is fundamental in geometry and various practical applications. Each regular polygon possesses specific interior and exterior angles that can be systematically calculated. The interior angle is the angle inside the polygon formed by two adjacent sides, while the exterior angle is formed by one side and an extension of an adjacent side. A key property is that an interior angle and its corresponding exterior angle always sum to 180 degrees. The sum of all interior angles for a polygon with 'n' sides is given by the formula (n - 2) * 180 degrees, and each individual interior angle is this sum divided by 'n'. Interestingly, the sum of all exterior angles for any convex polygon, regular or irregular, is always 360 degrees. These calculations are crucial not only for academic study but also in fields like architecture, engineering, and computer graphics for designing structures and rendering shapes.