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Sum of interior angle of a hexagon. (6-side polygon)  thx

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fahadsm | Student, Undergraduate | eNotes Newbie

Posted December 9, 2009 at 11:05 PM via web

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Sum of interior angle of a hexagon. (6-side polygon)

 

thx

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neela | High School Teacher | (Level 3) Valedictorian

Posted December 10, 2009 at 12:17 AM (Answer #1)

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The sum of the interior angles of a hexagon is 720 dgrees.

You can have 6 triangles in a hexagon if you join vertices to the centre. So on account six triangles 6*180 degrees minus the angle at the centre which is 360. or 180*6-360 = 720 degrees is the sum of the interor angles of a six sided  polygon  or hexagon.

In a hexagon,ABCDEFA, join AD, now the sum of interior angles of ABCDEFA is equal to the sum of the interior angles of 2 quadrolaterals,ABCD and ADEF or 360+360 =720 degrees.

You can also think, if ABCDEFA is a hexagon, then the hexagon contains triangle ABC+triangleDEF +a qdrilateral ACDF whose  sum of interior angles is equal to the interior angles of the hexagon.But the sum of the angles of two triangles and a quadrilateral is 2*180+360 dgrees = 720 degrees.Therefore, the sum of the interir angles of a hexagon is 720 degrees.

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krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted December 10, 2009 at 12:17 AM (Answer #2)

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Sum of interior angles of any polygon of having n sides sides equal to 2n-4 right angles.

A hexagon has 6 sides, or we can say for a hexagon n = 6.

Therefore sum of internal angles of a hexagon is:

= 2*6 - 4 = 12 - 4 = 8 right angles.

In degrees this can be represented as 8*90 = 720 degrees.

In this way we can calculate the sum of interior angles of different polygons as follows:

Triangle --> 2*3 - 4 = 6 - 4 = 2 Right Angles.

Rectangle --> 2*4 - 4 = 8 - 4 = 4 Right Angles.

Pentagon --> 2*5 - 4 = 10 - 4 = 6 Right Angles.

Octagon --> 2*8 - 4 = 16 - 4 = 12 Right Angles.

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