Question
Construct an angle of 60° with the help of compasses and bisect it by paper folding.

Answer

Draw a ray OA. With convenient radius and centre O, draw an arc cutting the ray OA at P. With the same radius and centre at P, draw another arc cutting the previous arc at Q. Draw OQ and extend it to B. $\angle\text{AOB}$ is the required angle of 60°.
We cut the part of paper as sector OPQ. Now, fold the part of paper such that line segments OP and OQ get coincided. Angle made at point O is the required angle, which is half of angle $\angle\text{AOB}.$

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