Why do a triangle's angles add up to 180°?

0:01 Draw any triangle. Tiny or huge, pointy or flat.

0:05 Add up its three angles, and you always get the same number. Why?

0:11 Let's find out, with a paper triangle and a pair of scissors.

0:17 Colour the three corners. Then tear them off.

0:22 Put the three points together, side by side.

0:26 Look. They fit exactly along a straight line.

0:30 A straight line is half a turn: one hundred and eighty degrees. So the three angles add up to one hundred and eighty.

0:43 Here's why it never fails. Draw a line through the top corner, parallel to the bottom side.

0:50 The left angle appears again, up here. And the right angle appears here.

0:59 Together with the top angle, they fill the straight line.

1:05 Stretch the triangle any way you like. The angles change, but the total stays one hundred and eighty.

1:14 So if two angles are sixty and fifty degrees, the third is one eighty, minus one hundred and ten, which makes seventy degrees.

1:24 Three corners. One straight line. Always one hundred and eighty.