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Question
In a convex hexagon prove that the sum of all interior angle is equal to the twice the sum of its exterior angle formed by producing the sides in the same order
In a convex hexagon prove that the sum of all interior angle is equal to the twice the sum of its exterior angle formed by producing the sides in the same order
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Solution
Sol:
In a hexagon number of sides = 6.
∴ Sum of the interior angles of a hexagon = (2n - 4) x 90°
= ( 2x 6 - 4) x 90° = 8 x 90° = 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 2 x 360°.= 720° -----(2)
from (1) and (2) we get
∴ In a convex hexagon, the sum of all interior angle is equal to twice the sum of its exterior angles.
In a hexagon number of sides = 6.
∴ Sum of the interior angles of a hexagon = (2n - 4) x 90°
= ( 2x 6 - 4) x 90° = 8 x 90° = 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 2 x 360°.= 720° -----(2)
from (1) and (2) we get
∴ In a convex hexagon, the sum of all interior angle is equal to twice the sum of its exterior angles.
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