Question

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

Answer 1

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.

Answer 2

Answer:

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 plygon is 360°

Therefoe sum of interior angles of a hexagon = twice the sum of interior angles.

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