Angles, triangles and polygons · Pulse Beat
The three angles inside any flat triangle add up to 180°. To see why, draw a line through one corner parallel to the opposite side. The angles on that line, which add to 180°, match the triangle's ang
The three angles inside any flat triangle add up to 180°. To see why, draw a line through one corner parallel to the opposite side. The angles on that line, which add to 180°, match the triangle's angles by alternate angles.
A polygon with n sides can be cut into (n − 2) triangles from one corner, so its angles add up to (n − 2) × 180°. A square (n = 4): 360°. A hexagon: 720°. Each angle of a regular polygon is that total divided by n: 90° for a square, 120° for a regular hexagon, 108° for a regular pentagon.
Triangles are special because they are rigid: with three fixed side lengths, the shape cannot change. That is why bridges, roof trusses and bike frames are built from triangles.