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please can you help me to know how to make an angle of 60 degree with compass as early as possible?

Hi!
Here is the answer to your question.
 
Follow the given steps to construct an angle of 60°.
(1)  Draw a line l and mark two points O and Q on it.
(2)  Draw an arc of convenient radius, while taking point O as centre. Let it intersect line l at R.
(3)  Taking R as centre and with the same radius as before, draw an arc intersecting the  previously drawn arc at S.
(4)  Join OS, which is the ray making 60° with the line l.
In this way ∠SOQ = 60° is constructed.
 
Best wishes!

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1. Draw a line segment which will become one side of the angle. (Skip this step if you are given this line.) The exact length is not important. Label it PQ. P will be the angle's vertex.Geometry construction with compass and straightedge or ruler or ruler
2. Set the compass on P, and set its width to any convenient setting.Geometry construction with compass and straightedge or ruler or ruler
3. Draw an arc across PQ and up over above the point P.Geometry construction with compass and straightedge or ruler or ruler
4. Without changing the compass width, move the compass to the point where the arc crosses PQ, and make an arc that crosses the first one.Geometry construction with compass and straightedge or ruler or ruler
5. Draw a line from P, through the intersection of the two arcs.Geometry construction with compass and straightedge or ruler or ruler
6. Done. The angle QPR has a measure of 60°Geometry construction with compass and straightedge or ruler or ruler

Proof

This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. The image below is the final drawing above with the red items added.

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Tnx!

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