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Question

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

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Solution

In a hexagon number of sides=6
Sum of interior angles of a hexagon=(2×64)×90°=8×90°=720°
Sum of exterior angle of a hexagon =360°
2 times the sum of exterior angles of hexagon =2×360=720
From (1)&(2)
In a convex hexagon the sum of all interior angle is equal to twice of exterior angles.

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