What is the sum of this polygon's interior angles?

What is the sum of this polygon's interior angles?

There are a couple ways to approach this problem.

 there are 180 degrees in a triangle.

Since this polygon has 5 sides, we can draw 5 triangles that all meet in the center.

Subtract 360 degrees because the circle in the middle is extra.




5×180∘−360∘
=540∘

An alternative approach is shown below.

make 3 triangle from the corner of the polygon

  3 x 180=540

540∘

540∘

    Sum of interior angles of a polygon: Showing a generalized way to find the sum of the interior angles of any polygon