Question

How to construct 60 degree angle using compass

Answer 1

We know that the angles in an equilateral triangle are all 60º in size.  This suggests that to construct a 60º angle we need to construct an equilateral triangle as described below.

Step 1:  Draw the arm PQ.
Step 2:  Place the point of the compass at P and draw an arcthat passes through Q.
Step 3:  Place the point of the compass at Q and draw an arc that passes through P.  Let this arc cut the arc drawn in Step 2 at R.

Answer 2

Draw a line AB
Taking A as centre draw an arc intersecting the AB
Now taking D as centre bisect the arc at E.
Now draw a ray from A towards
E.
Now it came out
To verify measure it.

Hopes it help.