How can you determine the sum of the interior angles of a hexagon justify your answer?

Answer 1

The sum of the interior angles of any n-sided figure is (2n - 4) right angles.

When n = 6 this equates to 8 x 90 ie 720o.

Consider an n-sided polygon. From any point A inside the polygon draw a straight line to each vertex, thus creating n triangles. (As the final formula is based on right angles, we work on right angles from here.)

Each triangle contains 180o, ie two right angles, so the sum of the angles of all the triangles is 2n right angles. The angles round the point A form a complete revolution, ie 360o, which is four right angles, which are not part of the interior angles of the polygon.

These interior angles therefore total (2n -4) right angles.