Here is a triangle. Before we work anything out: if I told you two of its angles, do you think you could work out the third one without measuring it? Have a think.

The interactive shows five shapes, one at a time: three triangles, then two four-sided shapes. Keep your eye on the total of the angles each time. What do you notice?

Today we drag the corners of a triangle and watch its angles change on the board. We'll pull one vertex to make it tall and pointy, then squash it flat and wide, then twist it into a shape none of us have seen before. Each time, before the numbers settle, predict what the total of the three angles will do.

First, the paper part. Cut or tear out a paper triangle, tear off its three corners, and line the three points up against a ruler — watch them make one straight line. A straight line is 180°, so that is our rule proved with paper. If your torn corners don't quite make a perfect straight line, that is just our scissors and fingers wobbling — a real triangle can never truly disagree with the rule.

Before we finish, we do one four-sided shape together on the board so you see the same method with 360°. A quadrilateral has angles 85°, 100°, 70°, and one missing. Add the three you know: 85° + 100° + 70° = 255°. Then subtract that total from 360°: 360° − 255° = 105°. So the missing angle is 105°. Same idea as the triangles, just take the known angles from 360° instead of 180°.