What is the sum of the measures of the interior angles of an octagon?

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Jan 1, 2017

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In the figure above we have an irregular octagon #ABCDEFGH#.

5 diagonals each originating from A are drawn.These diagonals divide the octagon into 6 triangles.

It is obvious from the figure that the sum of the measures of the interior angles of the octagon is equal to the sum of the interior angles of 6 triangles.

As we know that sum of the interior angles of a triangle is #180^@#, the sum of 8 interior angles of octagon will be #6xx180^@=1080^@#

Extension

Comparing with this situation we can say that a polygon of n-sides can be divided into #n-2# triangles and thereby the sum of the interior angles of polygon of n-sides will be

#=(n-2)xx180^@#

Exercise

How will you get the sum of 8 interior angles of a concave irregular octagon using following figure?

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