It is a lot easier than copying angles I will show you the steps to bisect an acute angle. The steps are still the same when the angle is right or obtuse.

Therefore, study the steps outlined here carefully and you will be able to bisect any angle.

Bisect Angle A:

Place the needle of the compass at vertex A and draw an arc of any size

Call the points where the arc intersects the rays, B and C.

Open the opening of your compass to a distance greater than the distance you used to draw the arc above.

Then, keeping the opening of the compass the same, put the needle of the compass at B and draw and arc

And put the needle of the compass at C and draw and arc

You should get something like that.The two arcs intersetcs where you see the red spot.

Draw a line between the vertex of A and the red spot and you are done!