In a convex hexagon, prove that the sum of all interior angle is equal

1.	In a convex hexagon, prove that the sum of all interior angle is equal to twice the sum of its exterior angles formed by producing the sides in the same order.
Answer» By using the formulas, The sum of interior angles of a polygon = (n – 2) × 180° The sum of interior angles of a hexagon = (6 – 2) × 180° = 4 × 180° = 720° The Sum of exterior angle of a polygon is 360° ∴ Sum of interior angles of a hexagon = twice the sum of interior angles. Hence proved.

In a convex hexagon, prove that the sum of all interior angle is equal to twice the sum of its exterior angles formed by producing the sides in the same order.

Answer»

By using the formulas,

The sum of interior angles of a polygon = (n – 2) × 180°

The sum of interior angles of a hexagon = (6 – 2) × 180° = 4 × 180° = 720°

The Sum of exterior angle of a polygon is 360°

∴ Sum of interior angles of a hexagon = twice the sum of interior angles.

Hence proved.