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.

Explanation

To prove: The sum of all interior angles is equal to twice the sum of its exterior angles formed by producing the sides in the same order.
In a hexagon number of sides`= 6`.
`∴` Sum of the interior angles of a hexagon`=(2n-4)xx90@`

Sum of the interior angles of a hexagon`=(2xx6-4)xx90@=8xx90@=720@` -------(1)
Sum of the exterior angles of a hexagon` =360°`
Given that `2` times the sum of the exterior angles of a hexagon i.e `2xx360@=720@` -----(2)
Thus from equation (i) and (ii), we can say that,
`∴` In a convex hexagon, the sum of all interior angle is equal to twice the sum of its exterior angles.
Hence proved.