Question

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

Answer 1

Draw a ray OA.
With convenient radius and centre at 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.
$\angle$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 $\angle$AOB.