It is common knowledge that the sum of the angles in a triangle
is 180° but how about in polygons with a greater numbers of angles?
If we are given a convex polygon with n sides and S is the sum of
the measures of the interior angles then S = 180(n - 2).
Example
Find the sum of the measures of the interior angles in an
octagon.
The octagon has 8 sides and we plug this value into our
formula:
S = 180(8 - 2) = 1080°
Hence the sum of the measures of the interior angles in an
octagon is 1080°.
Another thing with convex polygons is that the sum of the
measures of the exterior angles is always 360°
Video lesson: Find the sum of the measures of
the interior angles in an hexagon