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