×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

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

1 Answer
Jan 1, 2017

image.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.com