Symmetry of polygons, interior and exterior angles
Count the lines of symmetry of regular polygons, find the angle at each corner and see why the exterior angles always add up to 360 degrees.
- Iran: grade 8
- Russia: grade 7
Guide
This studio follows the Iranian Grade 8 lessons on polygons and symmetry, interior angles and exterior angles. A polygon is a closed broken line whose sides meet only at the corners. If all sides and all angles are equal, it is a regular polygon.
A regular polygon has line of symmetrys: a triangle 3, a square 4, a pentagon 5, and so on. A regular n-gon has n lines of symmetry.
The interior angles of an n-sided polygon add up to (n − 2)×180 degrees. In a regular polygon all angles are equal, so each angle is that total divided by n.
If you extend one side beyond a corner, the angle between the extension and the next side is the exterior angle. The interior and exterior angle at a corner lie side by side on a straight line: they add up to 180 degrees.
The exterior angles of any convex polygon (one at each corner) always add up to 360 degrees: n×180 − (n − 2)×180 = 360.