If all sides of a polygon are equal, it is called a regular polygon.
A six-sided figure is called a hexagon.
A seven-sided figure is called a heptagon.
An eight-sided figure is called an octagon, etc.
Theorem 1:
In a convex polygon of n sides, the sum of the interior angles is equal to (2n – 4) right angles.
Theorem 2:
In a convex polygon of n sides, the sum of the exterior angles, sides produced in order, is equal to 4 right angles.
If ‘n’ be the number of sides.
Each interior angle = ((2n–4)/n) right angles.
Sum of all the interior angles of a polygon of n sides = (n – 2) × 180° where (n ≥ 3)
For,
n = 3 (Triangle) ⇒ 180°
n = 4 (Rectangle) ⇒ 2 × 180° = 360°
n = 5 (Pentagon) ⇒ 3 × 180° = 540°
n = 6 (Hexagon) ⇒ 4 × 180° = 720°
Each interior angle of a regular polygon having n sides = ((n–2) × 180°)/n.
For,
n = 3 (Triangle) ⇒(180°/3) = 60°
n = 4 (Rectangle) ⇒ ((2×180°)/4) = 90°
n = 5 (Pentagon) ⇒ ((3×180°)/5) = 108°
n = 6 (Hexagon) ⇒ ((4×180°)/6) = 120°
Sum of all the exterior angles formed by producing the sides of polygon = 360°
a + b + c + d + e + f = 360°
Number of sides of polygon = (360°) / 180° – each interior angle
