Question

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 1

In a hexagon number of sides $=6$

Since the sum of interior angles of a hexagon $=(2n-4)\times {90}^o$

$=(2\times 6-4)\times {90}^0=8\times {90}^0={720}^0$

Sum of an exterior angle of a hexagon $={360}^0$

$2$ times the sum of exterior angles of hexagon $=2\times 360={720}^0$

From (1) & (2)

In a convex hexagon, the sum of all interior the angle is equal to twice of exterior angles.