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

1 Answer
P dilip_k ยท EZ as pi
Jan 1, 2017

image.mathcaptain.comimage.mathcaptain.com

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?

image.mathcaptain.comimage.mathcaptain.com

Related questions
See all questions in Angles with Triangles and Polygons
Impact of this question
20656 views around the world
You can reuse this answer
Creative Commons License