Is it possible to bisect any given angle using only a straightedge and a compas?
Yes
Set the compass at a reasonable width.
Put the point of the compass on the point of the angle.
Draw an arc on each arm of the angle.
With the point of the compass on where one arc intersects one
arm of the angle, draw a further arc between the arms of the angle
(roughly in the middle).
With the point of the compass on the other arc-arm intersection,
draw another arc to intersect this just drawn arc.
With a straight edge join this intersection to the point of the
angle - this line bisects the angle.