A paper protractor

Make your own protractor by folding paper. Draw a circle and cut it out: a whole circle is one full turn, 360°. Fold it into two equal halves and cut along the crease to get a semicircle. Write 0° at the bottom right corner. Half a turn is 180°, so write 180° at the bottom left corner.

Fold the semicircle in half to make a quarter circle. A quarter turn is half of 180°: 90°. Mark 90° at the top, on the crease.

Fold again. Now you have one eighth of a full turn: half of 90°, which is 45°. Unfold: there are two new creases. One is 45° from the 0° corner, so mark it 45°. The other is 45° from the 180° corner, so it reads 180° − 45° = 135°.

One more half fold gives half of 45°: 22.5°. Unfold, and the creases are at 22.5°, 45°, 67.5°, 90°, 112.5°, 135° and 157.5°. They cut the straight angle into 8 equal angles, ∠AOB = ∠BOC = … = ∠HOI, each 180° ÷ 8 = 22.5°.

Every time, you folded an angle in half. Cutting an angle into two equal angles is called bisecting it, and the line that does it (here, the crease) is the angle bisector.