Q103 of 160 Page 144

State whether the statements are true (T) or false (F).

If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon. then it is hexagon.

TRUE

In a hexagon number of sides = 6.


∴ Sum of the interior angles of a hexagon = (2n - 4) x 90°


= (2 x 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 ie. 2 x 360°= 720° -----(2)


from (1) and (2) we get


∴ If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is hexagon.


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