The Triangle Rule

Why the angles add up to 180°

An interactive lesson with 9 steps, about 8 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The angles of any triangle add up to 180°. The proof uses a line parallel to one side.
• An exterior angle equals the sum of the two opposite interior angles.
• An $n$-sided polygon's interior angles add up to $(n-2) \times 180°$.

Steps

1. Drag the corners
2. Two right angles?
3. The proof
4. Missing angle
5. Isosceles
6. Exterior angle
7. Beyond triangles
8. Hexagon
9. Stop sign