Origami

Make a fold on half of a square paper as the first step for folding a regular hexagon or regular pentagon.
E is the midpoint of AC (as well as E' when part of AC is folded). F is the midpoint of EC and the red dotted line is perpendicular to AC at F.

To make a 60 deg at center (for folding a hexagon), fold E on the red line.
To make a 36 deg (approx.) at center (for folding a pentagon), fold to bisect AOF.
To make a 72 deg (approx.), but not at center (another method for pentagon), simply fold A to K, the midpoint of BC.

Arthur Lee, 28/4/2006, Created with GeoGebra